High Five, Pythagoras!
Number Theory
Level
1
A Pythagorean triple is a set of positive integers \(a < b < c\) such that \(a^2 + b^2 = c^2\). Some examples are \[\begin{align} 3^2 + 4^2 &= 5^2 \\ 5^2 + 12^2 &= 13^2 \\ 8^2 + 15^2 &= 17^2. \end{align}\] Note that each of these Pythagorean triples contains a multiple of 5.
How many Pythagorean triples \(\{a, b, c\}\) are there for which none of the three numbers is a multiple of 5 and \(c \leq 1000?\)
by
Arjen Vreugdenhil