Can a number be both a square number and an oblong number?

Answer 1

This user has never heard of such a thing as an oblong number. If you mean a number that equals the product of two different numbers other than 1, then yes: 36 = 6 x 6 = 4 x 9.

Or if you prefer, 100 = 10 x 10 = 5 x 20.

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this user over here says no, if you define an oblong number to be a positive number in the form n(n+1).

to say a number can be an oblong number and a square number is to say that there exists an n such that n2=n(n+1)

=n2 + n

so unless n=0, this statement is not true, and since the oblong number is positive, then it can't be zero.

why can't it be zero (or negative, for that matter)? well, these numbers originally popped up as a geometric picture; an oblong number number is a group of dots arranged in even rows or columns, where there was one more column than row, or vice versa. the number itself is the quantity of dots, which is always positive.

another way of thinking about it is by definition, an oblong number is a square minus a row or column, or a square plus a row or column, and thus, not a square.