Question

Find two such least consective numbers so that the difference of squares
of them is a perfect square number.
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Answer 1

Answer:

For any number “N”, let the pair of consecutive numbers be 2N(N+1) and 2N(N+1)+1.

The square root of the differences of their squares is 2N+1.

N , 2N(N+1) . 2N(N+1)+1 , 2N+1

0 , 2*0*(0+1)=0 , . . 1 , 2*0+1 = 1

1 ,. 2*1*(1+1) =4 . , . 5 , 2*1+1 = 3

2 , 2*2*(2+1) = 12 , 13 , 2*2+1 = 5

…

7 , 2*7*(7+1) = 112, 113 , 2*7+1 = 15

If you accept “0” then the least pair of consecutive numbers is 0 & 1.

Other wise the least pair of consecutive numbers is 4 & 5.

As pointed out in another answer, these sets of three numbers (4, 5 & 3, . . 112, 113 & 15, . . . ) fit the Pythagoras theorem and if used as the sides of a triangle, will form a right angled triangle.

Answer 2

Answer:

Cuba cynicism chicken bunk 7h hubbub 5×7/=788