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Triangular and Square Settlement (Posted on 2015-10-13) Difficulty: 3 of 5
A is a triangular number and B is a perfect square such that:
A – B = 2015

Find the four smallest values of A+B

No Solution Yet Submitted by K Sengupta    
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re(3): possible solution. //infinitely many ? | Comment 5 of 7 |
(In reply to re(2): possible solution. //infinitely many ? by broll)

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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