MathDB

3

Part of 2012 Dutch IMO TST

Problems(2)

\frac{a}{b} + \frac{a+1}{b+1} not an integer

Source: Dutch IMO TST1 2012 p3

1/10/2020
Determine all positive integers that cannot be written as ab+a+1b+1\frac{a}{b} + \frac{a+1}{b+1} where aa and bb are positive integers.
number theoryInteger
(x + y + 1) | 2xy and (x + y - 1) | (x^2 + y^2 - 1) , diophantine system

Source: Dutch IMO TST2 2012 p3

1/10/2020
Determine all pairs (x,y)(x, y) of positive integers satisfying x+y+1∣2xyx + y + 1 | 2xy and x+y−1∣x2+y2−1 x + y - 1 | x^2 + y^2 - 1.
Diophantine Equationsdiophantinenumber theory