Posted by **number theory** on Wednesday, March 27, 2013 at 1:11am.

What is the sum of all integer values of n satisfying 1≤n≤100, such that n2−1 is a product of exactly two distinct prime numbers?

- maths -
**Reiny**, Wednesday, March 27, 2013 at 9:59am
so we need to look at the number before a perfect square and see if it is a prime or not

4-1 = 3 , 1x3 , 1 is not considered prime

9-1 = 8 more than 1 pair of factors

16-1 = 15 --> 3x5 , both prime ✔

25-1 = 24 lots of pairs

36-1 = 35 --> 5x7 , both prime ✔

49-1 = 48 lots

64-1 = 63 lots

81 - 1 = 80 lots

100-1 = 99 lots

so the only n values are 4 and 6

and their sum is 10

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