Question 48

The number of different prime numbers $$p > 2$$ such that p divides $$71^2 - 37^2 - 51$$ is

Solution

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Going by the traditional method since the numbers are easy to calculate, the value of $$71^2 - 37^2 - 51$$ is 3621.

The prime factorisation of 3621 is $$\ 1\times\ 3\times\ 17\times\ 71$$

Hence, there are three prime numbers that divide the expression.

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