Inspired by Calvin Lin

Number Theory Level 4

A primitive pythagorean triplet is a set of three positive integer { a , b , c } \{ a, b, c \} which are mutually prime and satisfy a 2 + b 2 = c 2 a^2 + b^2 = c^2 .

How many such triplets exist such that 1 ≤ c ≤ 100 1 \leq c \leq 100 and none of a , b , c a, b, c are prime?


The answer is 3.

Shib Shankar Sikder by Shib Shankar Sikder , 34, India

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1 solution

Tom Van Lier
Nov 11, 2015

I think there are 3 :

(16, 63, 65) (33, 56, 65) and (36, 77, 85). Therefore, this question has a wrong answer, since there are at least 3 (I think they're the only one, but didn't prove this though.)

Note : I lost points for 3 being a wrong answer and for 6 (swapping a and b, because they shouldn't be ordered).

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Thanks. I have updated the answer to 3.

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Calvin Lin Staff - 5 years, 6 months ago

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