1964 IMO Problems/Problem 1
(a) Find all positive integers for which is divisible by .
(b) Prove that there is no positive integer for which is divisible by .
We see that is equivalent to and for congruent to , , and , respectively.
(a) From the statement above, only divisible by work.
(b) Again from the statement above, can never be congruent to , so there are no solutions for .