Question: The 503rd Infantry Regiment and the 2nd Infantry Division are both formations of what military branch

Context paragraphs:
37th Field Artillery Regiment: The 37th Field Artillery Regiment is a field artillery regiment of the United States Army, and parent regiment under the U.S. Army Regimental System.  The regiment was first constituted 5 July 1918 in the National Army.  The regiment served with the 10th Division during World War I, and the 2nd Infantry Division during World War II.  Elements of the regiment have served with the 2nd Infantry Division, 6th Infantry Division, 79th Infantry Division, and 172nd Infantry Brigade, among other units.  Two battalions of the regiment are currently active, the 1st Battalion, 37th Field Artillery is the direct support cannon battalion, in support of the 1st Stryker Brigade Combat Team, 2nd Infantry Division and the 6th Battalion, 37th Field Artillery is a Multiple Launch Rocket System battalion in the 210th Field Artillery Brigade.

503rd Infantry Regiment (United States): The 503rd Infantry Regiment, formerly the 503rd Parachute Infantry Regiment (PIR) and the 503rd Airborne Infantry Regiment (AIR), is an airborne infantry regiment of the United States Army.  The regiment served as an independent regiment in the Pacific War during World War II; at Fort Campbell, Kentucky; in Okinawa, Japan; and in Germany.  Regimental elements have been assigned to the 2nd Infantry Division, the 11th Airborne Division, the 24th Infantry Division, the 82nd Airborne Division, and the 173rd Airborne Brigade Combat Team.  Regimental elements have participated in campaigns in the Vietnam War, Operation Enduring Freedom–Afghanistan, and Operation Iraqi Freedom.  The regiment claims 15 Medal of Honor recipients: two from World War II, 10 from Vietnam, and three from Afghanistan.  A parent regiment under the U.S. Army Regimental System.  The regiment's 1st and 2nd Battalions are active, assigned to the 173rd Airborne Brigade, based at Caserma Ederle, Vicenza, Italy.

52nd Infantry Division (German Empire): The 52nd Infantry Division ("52.Infanterie-Division") was a division of the Imperial German Army during World War I.  The division was formed on March 6, 1915, from units taken from other divisions or newly raised.  The division was initially mixed, with two infantry regiments from the Grand Duchy of Baden, one infantry regiment from Prussian Saxony, and Prussian and Baden support units (cavalry, artillery, engineers, and service and support units).  While the infantry regiments and the divisional cavalry squadron were regular army units, the rest of the division was made up of reserve units and units formed during the war.  The 66th Magdeburg Infantry Regiment was taken from the 7th Infantry Division, and the 169th and 170th Infantry Regiments were taken from Baden's 29th Infantry Division.  The 52nd Infantry Division became more Baden as the war progressed, as the 66th Magdeburg Infantry Regiment, the regiment from Prussian Saxony, was replaced on April 6, 1917, by Baden's 111th Infantry Regiment "Margrave Ludwig Wilhelm".

2nd Infantry Division (United States): The 2nd Infantry Division ("Indianhead"; "2ID," "2nd ID", or "Second D") is a formation of the United States Army.  Its current primary mission is the defense of South Korea in the initial stages of an invasion from North Korea until other American units can arrive.  There are approximately 17,000 soldiers in the 2nd Infantry Division, with 10,000 of them stationed in South Korea, accounting for about 35% of the United States Forces Korea personnel.

502nd Infantry Regiment (United States): The 502nd Infantry Regiment (502nd INF), previously titled the 502nd Parachute Infantry Regiment (502nd PIR), is an airborne infantry regiment of the United States Army.  The regiment was established shortly after the American entry into World War II, and was assigned as a regiment of the 101st Airborne Division, "The Screaming Eagles", one of the most decorated formations of the U.S. Army.  The regiment saw substantial action in the European Theater of World War II and was deactivated in 1945, shortly after the end of the war.  Reactivating in a new form in 1956, the 502nd Infantry has served in the Vietnam War, the first Gulf War, Operation Iraqi Freedom, Operation Enduring Freedom in Afghanistan, and Operation Inherent Resolve in Iraq.  It was removed from parachute status with the rest of the 101st Airborne Division in 1969, and since 1974, the regiment has been classified as an Air Assault unit.  Currently, its 1st and 2nd battalions are active.  Both battalions are assigned to the 2nd Brigade Combat Team, 101st Airborne Division (Air Assault).

3rd Infantry Brigade, 2nd Infantry Division: At the time of its activation, the 2nd Infantry Division was composed of the 3rd Infantry Brigade, which included the 9th Infantry Regiment; the 23rd Infantry Regiment and the 5th Machine Gun Battalion; the 4th Marine Brigade, which consisted of the 5th Marine Regiment, the 6th Marine Regiment and the 6th Machine Gun Battalion; 2nd Brigade of field artillery; and various supporting units.

153rd Infantry Regiment (United States): The 153d Infantry Regiment (First Arkansas) is a United States infantry regiment, currently represented in the Arkansas Army National Guard by the 1st Battalion, 153rd Infantry, headquartered at Malvern, Arkansas, and 2nd Battalion, 153rd Infantry, headquartered at Searcy, Arkansas, elements of the 39th Brigade Combat Team.  The regiment was also represented by the 3rd Battalion, 153rd Infantry Regiment headquartered at Warren, Arkansas until that unit was deactivated on 5 September 2005.  The regiment was activated as the 1st Arkansas Volunteer Infantry for the Spanish-American War, but did not deploy overseas.  The regiment was activated for World War I, redesignated as the 153rd Infantry and shipped to France as a part of the 39th Division, but became a replacement division and personnel were reassigned to other AEF units.  The regiment was activated for World War II and deployed to the Aleutian Islands, participating in the Aleutian Islands Campaign.  Recently, elements of the regiment have participated in two deployments in support of Operation Iraqi Freedom, in 2004 and again in 2008.

2nd Battalion, 503rd Infantry Regiment: The 2nd Battalion, 503rd Infantry Regiment (2-503rd) is an active duty airborne infantry battalion in the United States Army, assigned to the 173rd Airborne Brigade Combat Team and stationed at Caserma Ederle, Vicenza, Italy.  The battalion has served with the 2nd Infantry Division, the 11th Airborne Division, the 24th Infantry Division, the 82nd Airborne Division, and the 173rd Airborne Brigade; has been stationed in Korea, Germany, Italy and the United States; and earned campaign credits in World War II, the Vietnam War, Operation Enduring Freedom-Afghanistan, and Operation Iraqi Freedom.

Operation Murfreesboro: In October 2006, the 1st Battalion, 9th Infantry Regiment (1-9 IN) deployed to east Ramadi for the 2nd Brigade of the 2nd Infantry Division's second tour to Iraq.  The "Manchus" were replacing the 506th Infantry Regiment (506 AR) from the 101st Airborne Division, and the 1st Armored Division (1 AD).  Many soldiers of the new battalion had previously been in east Ramadi during a 2004-2005 deployment under the colors of the 503rd Infantry Regiment (1-503 IN), thus giving the Americans a slight advantage in that many of the battalion's non-commissioned officers were already familiar with the terrain.

1st Battalion, 503rd Infantry Regiment: The 1st Battalion, 503rd Infantry Regiment (1-503rd) is an active duty airborne infantry battalion in the United States Army, assigned to the 173rd Airborne Brigade Combat Team and stationed in Vicennza, Italy.  The battalion has served with the 2nd Infantry Division, the 11th Airborne Division, the 24th Infantry Division, the 82nd Airborne Division, and the 173rd Airborne Brigade; has been stationed in Korea, Italy and the United States; and earned campaign credits in World War II, the Vietnam War, Operation Enduring Freedom-Afghanistan, and Operation Iraqi Freedom.

Supporting paragraphs: 503rd Infantry Regiment (United States) 2nd Infantry Division (United States)
Answer: United States Army