Arithmetic+ 04: UNIZOR.COM - Math+ &Problems - Arithmetic
Channel: Zor Shekhtman on UNIZOR Education
Date: 2024-02-17

UNIZOR.COM - Creative Mind through Art of Mathematics
Read full text of notes for this lecture on UNIZOR.COM - Math+ &Problems - Arithmetic - Arithmetic+ 04.

Notes to a video lecture on http://www.unizor.com

Arithmetic+ 04

Problem A
Consider two numbers:
X=11111111 (digit 1 repeats 8 times) and
Y=11111...11111 (digit 1 repeats 100 times).
What is their greatest common factor?

Problem B
Prove that a remainder of the division of some natural number by 9 is the same as a remainder of the division by 9 of the sum of this number's digits.

Problem C
Prove that if the sum of digits of some natural number N is the same as the sum of digits of the number 2·N then number N is divisible by 9.