Question

____is common number among square and triangular number​

Answer 1

Answer:

8, 6), (49, 35), (288, 204), ... (OEIS A001108 and A001109), corresponding to the triangular square numbers 1, 36, 1225, 41616, 1413721, 48024900

Answer 2

Answer:

A number which is simultaneously square and triangular. Let Tₙ denote the nth triangular number and Sₘ the mth square number, then a number which is both triangular and square satisfies the equation Tₙ=Sₘ

Step-by-step explanation:

1/2n(n+1)=m².

Simplifying this we get the Pell equation

x²-2y²=1  

(x,y)= (3,2), (17, 12), (99, 70), (577, 408),.... are the first few solutions.

These result in the solutions (n,m)=(1,1), (8, 6), (49, 35), (288, 204),... which correspond to the triangular square numbers 1, 36, 1225, 41616, 1413721, 48024900, etc.

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