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Primes divide expression? (Posted on 2016-07-20) Difficulty: 3 of 5
Define funcitons F, G and H:
F(x,y) = x2 - 2xy + y2 - 5x + 7y
G(x,y) = x2 - 3xy + 2y2 + x - y
H(x,y) = xy - 12x + 15y

If x and y are integers and p is an odd prime such that the values of F(x,y) and G(x,y) are both divisible by p, then prove that H(x,y) is also divisible by p.

Seventeen divides expression? is a specific instance of this puzzle where p=17.

No Solution Yet Submitted by Brian Smith    
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  Subject Author Date
Other similar wayarmando2016-07-22 04:10:53
Some ThoughtsNice problembroll2016-07-21 00:05:20
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