perplexus.info :: Numbers : Some Near Pythagorean Integers Sum to Squares

Some Near Pythagorean Integers Sum to Squares (Posted on 2023-08-11)

Consider five positive integers a, b, c, d, and p, with gcd(a,b,c)=1, that satisfy this system of equations:

a, b, and c are different positive integers.
a²+b²+c²=d²
a+b+c=p²

Determine the four smallest values of a+b+c+d+p.

*** Computer program/excel solver assisted solutions are welcome, but a semi-analytic (p&p and hand calculator) methodology is preferred.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

The four smallest values of a+b+c+d+p are: 49,85,87, and 89.
For an explanation, refer to the solution submitted by Charlie in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
No Subject	K Sengupta	2023-09-06 00:28:06
HEalth	Rudyard Nolan	2023-09-05 19:59:10
computer solution	Charlie	2023-08-11 09:01:04

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