when "n" is composite is known as a "Fermat liar". If we do pick an "a" such that
then "a" is known as a "Fermat witness" for the compositeness of "n".
"formula_5" is the modulo operation. Its result is what remains, if p is divided by n. As an example,
The RSA algorithm for public-key encryption can be done in such a way that it uses this test. This is useful in cryptography.
Hash function
The Hash function is a function. When a computer program is written, very often, large amounts of data need to be stored. These are normally stored as hash tables. In order to find the data again, some value is calculated. This is like when someone reads a book, and to remember, they put what they read into their own words. Hash values are much the same, except that care is taken that different sets of data do not get the same hash value (this is called a "hash collision").
A cryptographic hash function is a kind that is used in cryptography. Its hash value is a fixed-size, alphanumeric string, and may also be called a 'message digest', 'digital fingerprint', 'digest' or 'checksum'.
Hash table
Trinity
In the Christian religion, the Trinity is an idea used to explain that three different "persons" are called God: God the Father, God the Son, and God the Holy Spirit (who is sometimes called the "Holy Ghost"). Trinity states that these three all form the same God.
The Oxford Dictionary of the Christian Church describes the Trinity as "the central dogma of Christian theology".
Before the idea was made dogma, at the First Council of Nicaea, there were also other ideas on how to solve the problem. These included:
The English word "Trinity" comes from Latin "Trinitas", meaning "the number three". This abstract noun is formed from the adjective "trinus" (three each, threefold, triple), as the word "unitas" is the abstract noun formed from "unus" (one).
The corresponding word in Greek is "" ("Trias"), meaning "a set of three" or "the number three."
The first recorded use of this Greek word in Christian theology was by Theophilus of Antioch in about 170. He did not speak about the Trinity of god. He wrote: "In like manner also the three days which were before the luminaries, are types of the Trinity [], of God, and His Word, and His wisdom. And the fourth is the type of man, who needs light, that so there may be God, the Word, wisdom, man."
Tertullian, a Latin theologian who wrote in the early third century, was the first to use "Trinity" "person" and "substance" to explain that the Father, Son and Holy Spirit are "one in essence – not one in Person."
About a century later, in 325, the First Council of Nicaea established the doctrine of the Trinity as orthodoxy and adopted the Nicene Creed that described Christ as "God of God, Light of Light, very God of very God, begotten, not made, being of one substance ("homoousios") with the Father."
Many but not all Christians worship God in the form of the Trinity. In the Old Testament there are several places where there seems to be evidence for a Trinity. Genesis 1:26 states that God said "Let us make man in our image". Deuteronomy 6:4 states that “The Lord our God is one Lord”. The word that has been translated as "one" can also be translated as "united".
The Trinity is also implied in the New Testament, though that term is not used. Jesus never explained it fully in his teaching to people, but made a number of claims to be God. The disciple John was one of Jesus' best friends on Earth, so understood Jesus better than many other people. He starts his gospel by saying "In the beginning was the Word. The Word was with God, and the Word was God." He calls Jesus 'the Word' because Jesus was how God told people about himself. In John 8:58, Jesus said "before Abraham was even born, I AM!" I AM is what God said his name was to Moses, meaning that he is always there anywhere in time or space. In John 10:30 and 10:38, he tells people "The Father and I are one." and "the Father is in me, and I am in the Father." Lastly, he forgave people for sins, which only God can do.
When Jesus came the early Christians had to make sense of the fact that God had come among them through the power of the Holy Spirit. Matthew wrote in his gospel: “Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit (Matthew 28:19). Several things in the gospel of John are often thought to point to a God who is more than just one being. The three persons of God are also mentioned in the second book of Corinthians.
It was several hundred years after the life of Jesus before many Christians accepted the idea that God was a Trinity. It was a difficult idea, because the Hebrew scriptures talk about God being One. The Greeks and the Romans could only understand Christ as a person who was bringing God’s Word. It was not until the 4th century that the three were recognised as being the three parts of one whole God. This was decided by the Council of Nicaea in 325. By the end of the century many Christians had been swayed to believe in God as a Trinity.
In the 5th century Saint Patrick brought Christianity to Ireland. There is an old Irish legend which says that Patrick used the shamrock to explain the idea of the Trinity. The shamrock has three small leaves. Patrick told the people that the three leaves represented God the Father, God the Son and God the Holy Spirit. He said that the whole plant represented God.
In Christian churches the Sunday after Pentecost (the 50th day after Easter) is called the “Feast of the Holy Trinity”. This feast probably started in the 10th century. In 1334 Pope John XXII made it official for the whole church. In the Anglican and Lutheran Churches the weeks that follow The Feast of the Trinity are dated according to how many weeks after Trinity they are (e.g. the 20th Sunday after Trinity). In the Roman liturgy these Sundays are dated “after Pentecoste” (e.g. the 21st Sunday after Pentecoste).
Islam teaches that God is indivisible (can not be divided). For this reason, several verses of the Qur'an teach that the doctrine of Trinity is blasphemous (against God). The concept of the Trinity in Meitei religion also exist as Mangang Luwang Khuman.
Mošovce
Mošovce is one of the biggest villages in the Turiec Region of Slovakia.
Mošovce has existed for 770 years. In this time people built many old and beautiful buildings. King Andrew II wrote about the village for the first time in 1233.
At first, "Mošovce" had two parts: The first one, "Machyuch", was in the area of today’s "Starý Rad" Street. The village took its today's name from the second part, "Terra Moys", which was in the place of the present day "Vidrmoch" Street. Because of the name of the second part, which means "The Land of Mojš", we believe that all the village was the property of a certain Mr. "Mojš". His name could be a short form of a longer Slavic name "Mojtech", similar to the names "Vojtech" or "Mojmír". In the history the name of the village changed from "Mossovych", "Mosocz", "Mossowecz", "villa regia Mayos alio nomine Mossovych", "oppidioum Mayus sue Mosocz", "Mosocz olim Mayus" to the present-day "Mošovce".
The name of a separate very old part of "Mošovce", "Chornukov", chaged to the modern form of "Čerňakov".
Mošovce was at first a royal village, and in about 1350 changed into a privileged town, which belonged to the royal castle of Blatnica. In 1527 the Révay family became its owners, and they took away the town privileges of "Mošovce" for almost 400 years.
In the past, Mošovce was an important craft center of the Turiec region. Crafts were very successful, and there were around 15 guilds in the town; the bootmaker and the most famous furrier guild existed for the longest time. The present-day Mošovce is an important tourist area with many interesting places.