- #1

ver_mathstats

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- Homework Statement
- Let a be an integer equal or greater than 0. Prove that at least one of the integers 9a+1, 9a+10, 9a+19 and 9a+28 is composite

- Relevant Equations
- euclidean algorithm

I am really struggling in how to begin this problem. So far I have considered using the Euclidean Algorithm and trying to find the gcd of each number like gcd(9,10) but each time they give me 1 so that doesn't work. My next idea is to do a proof by contradiction where I start with assuming that the integers are prime and somehow find a contradiction but I am unsure how to proceed.

Any help would be appreciated as I am really unsure of how to proceed. Thank you.

Any help would be appreciated as I am really unsure of how to proceed. Thank you.