- #1
geoffrey159
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Homework Statement
Prove that there are infinitely many prime numbers written ##ak+b##, with ##a,b,k## integers greater than 1
Homework Equations
The Attempt at a Solution
Please could you tell me if you agree with that proof ?
By contradiction:
Assume that there is an integer ##k## such that ##ak+b## is the greatest prime number of that sort. Then for any ##n > k##, there are ##(u,v)\in \mathbb{N}^\star## such that ##an+b = uv ##. Take ##n = k + u ##, therefore ## ak + b = u (v-a) ##, which contradicts the fact that ##ak+b## is prime.