Numbers in Pythagorean Form

Number Theory Level 3

$0 = a^2 + b^2 - c^2$

What is the smallest positive integer $n$ , such that there does not exist integers $a,b,c$ where

$n = a^2 + b^2 - c ^2 ?$

10000 \leq n

100 \leq n < 10000

1 \leq n < 100

All positive integers can be represented in this form

1 solution

Maria Kozlowska
Nov 14, 2016

Let $b=c+1$ . Then $b^2-c^2=2c+1$ . For $a=0, c \geq 0$ we cover all odd numbers, for $a=1, c \geq 0$ all even numbers.

We can also get all the negative integers in a similar way.

Calvin Lin Staff - 4 years, 7 months ago