Question

List the quadruples in the relation { a,b,c,d} where a, b, c, d are integers with

0 < a < b < c < d < 8.

Answer 1

A Pythagorean quadruple is a tuple of integers $a, b, c,$ and $d,$ such that $a^2 + b^2 + c^2 = d^2.$

$$1^2+2^2+3^2=14, No$$ $$1^2+2^2+4^2=21, No$$ $$1^2+2^2+5^2=30, No$$ $$1^2+2^2+6^2=41, No$$ $$1^2+3^2+4^2=26, No$$ $$1^2+3^2+5^2=35, No$$ $$1^2+3^2+6^2=46, No$$ $$1^2+4^2+5^2=42, No$$ $$1^2+4^2+6^2=53, No$$ $$1^2+5^2+6^2=62, No$$ $$1^2+6^2+7^2=86, No$$ $$2^2+3^2+4^2=29, No$$ $$2^2+3^2+5^2=38, No$$ $$2^2+3^2+6^2=49=7^2, Yes$$ $$2^2+4^2+5^2=45, No$$ $$2^2+4^2+6^2=56, No$$ $$2^2+5^2+6^2=65, No$$ $$3^2+4^2+5^2=50, No$$ $$3^2+4^2+6^2=61, No$$ $$3^2+5^2+6^2=70, No$$ $$4^2+5^2+6^2=77, No$$

$\{2,3,6,7\}$