Sample Question #40 (mathematics – number theory)

Can you show that, for any prime number *p* that is at least equal to 5, the value of *p*^{2}-1 is a multiple of 24 (i.e., wholly divisible by 24)?

[Taken from webpage "The Prime Puzzle"]

(Comment: I personally find questions like these appalling; unfortunately, they are extremely popular at quant interviews)

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Thanks, anonymous visitor. This is a pretty tough question, and it’s likely to be asked only of candidates who have a strong math background (e.g., math Ph.D. students or ex-math Olympiads competitors!).