Quandaries and Queries


My name is Ladis and I have an exercise that I do not know how to solve it. It says:
Three prime numbers p,q and r, all greater than 3, form an arithmetic progression: p=p, q=p+d and r= p+2d. Prove that d is divisible by 6.

It is clear that p and q are both odd numbers, then from q= p+d we get q-p=d and as q-p is an even number d is divisible by 2 but, how can I prove that d is also divisible by 3?
Please help me!



Hi Ladis,

One way to look at the problem is to treat p and d as mod 3 numbers: p, q, and r can only be 1 or 2 (mod 3) -- because that was given to you. So try d=1, 2, and 3.



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