Answer to Question #273370 in Discrete Mathematics for Joe

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 $a^2 + b^2 + c^2 = d^2.$

$$1^2+2^2+3^2=14, No$$

$$1^2+2^2+4^2=21, No$$

$$1^2+2^2+5^2=30, No$$

$$1^2+2^2+6^2=41, No$$

$$1^2+3^2+4^2=26, No$$

$$1^2+3^2+5^2=35, No$$

$$1^2+3^2+6^2=46, No$$

$$1^2+4^2+5^2=42, No$$

$$1^2+4^2+6^2=53, No$$

$$1^2+5^2+6^2=62, No$$

$$1^2+6^2+7^2=86, No$$

$$2^2+3^2+4^2=29, No$$

$$2^2+3^2+5^2=38, No$$

$$2^2+3^2+6^2=49=7^2, Yes$$

$$2^2+4^2+5^2=45, No$$

$$2^2+4^2+6^2=56, No$$

$$2^2+5^2+6^2=65, No$$

$$3^2+4^2+5^2=50, No$$

$$3^2+4^2+6^2=61, No$$

$$3^2+5^2+6^2=70, No$$

$$4^2+5^2+6^2=77, No$$

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