MathDB

11

Part of 2018 Hanoi Open Mathematics Competitions

Problems(2)

(xy + 2)^2 = x^2 + y^2 diophantine (HOMC 2018 Ind. p11)

Source:

1/31/2020
Find all pairs of nonnegative integers (x,y)(x, y) for which (xy+2)2=x2+y2(xy + 2)^2 = x^2 + y^2 .
Diophantine equationnumber theory
2^n + 11 is divisible by 2^k - 1 (HOMC 2018 ind. sen11)

Source:

2/2/2020
Find all positive integers kk such that there exists a positive integer nn, for which 2n+112^n + 11 is divisible by 2kāˆ’12^k - 1.
number theorydivisible