Basic Properties of Integer Divisibility
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- We say an integer d≠0d \ne 0d=0 divides an integer nnn if and only if there exists an integer ccc such that n=c⋅dn = c \cdot dn=c⋅d. In other words, nd\frac{n}{d}dn is an inte…
By Jeffery Yu, Tom Shen, Expii Team
- This is an introduction into number theory. Many people try to define it as "arithmetic of integers", but we aren't going to define and restrict the area of mathematics it cover…
By amaterasu, Andrew Wang, Hrishikesh Kamath, Victor Wang
- Without using congruence or brute force methods, prove that 232+12^{32}+1232+1 is divisible by 641641641.
By amaterasu
- If x,yx,yx,y are integers and aaa divides both bbb and ccc, prove that aaa divides any linear combination of bbb and ccc i.e. a∣bx+cya|bx+cya∣bx+cy.
By amaterasu