perplexus.info :: Just Math : Triangular and Square Settlement

Triangular and Square Settlement (Posted on 2015-10-13)

A is a triangular number and B is a perfect square such that:
A – B = 2015

Find the four smallest values of A+B

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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re(3): possible solution. //infinitely many ?

| Comment 5 of 7 |

let A=a(a+1)/2 and B=b^2 then we need

a(a+1)/2-b^2=2015

a^2+a-2b^2=4030

now using:

http://www.alpertron.com.ar/QUAD.HTM

we get the following generic solution

for any solution a,b we have another solution x,y

x=3a+4b+1

y=2a+3b+1

Thus there are indeed an infinite number of solutions

Posted by Daniel on 2015-10-14 07:11:46

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