MathDB

1

Part of 1985 Vietnam National Olympiad

Problems(2)

Find all pairs of integers

Source: Vietnam NMO 1985 Problem 1

2/12/2009
Find all pairs (x,y) (x, y) of integers such that x^3 \minus{} y^3 \equal{} 2xy \plus{} 8.
number theory unsolvednumber theory
Divisible problem

Source: Vietnam NMO 1985 Problem 4

2/12/2009
Let a a, b b and m m be positive integers. Prove that there exists a positive integer n n such that (a^n \minus{} 1)b is divisible by m m if and only if \gcd (ab, m) \equal{} \gcd (b, m).
number theory unsolvednumber theory