Three Easy Pieces

Number Theory Level 3

x x is divisible by 2, y y is divisible by 3, and z z is divisible by 5. What's the largest integer that must divide x y + y z + x z ? xy+yz+xz?


The answer is 1.

Jason Dyer by Jason Dyer

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1 solution

Paul Hindess
Dec 21, 2016

In the case where x=2, y=3 and z=5, xy + yz + xz = 31 which is prime. This is divisible by only 1 and 31.

Trying, say x = 4, y = 3, z = 5 gives an answer that is not divisible by 31' so the answer must be 1.

4 Helpful 0 Interesting 0 Brilliant 0 Confused

Because of the way this problem was written, your answer works fine -- you just need to exhibit one prime. Just out of curiosity, could you work out all the cases where xy+yz+xz is prime?

Jason Dyer Staff - 4 years, 4 months ago

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