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Trisquares refer to numbers that can be expressed as the sum of three squares. There are different classifications based on their properties, such as perfect trisquares, which are the sum of three perfect squares, and generalized trisquares, which may include non-integer solutions. Additionally, the concept can extend to specific sequences or patterns within the sums of three squares, like those found in number theory. Overall, trisquares encompass a variety of forms and applications in mathematical contexts.

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What is a trisquare?

A trisquare is a specific type of mathematical object that relates to the concept of squares and triangular numbers. It is defined as a number that can be expressed as the sum of the first ( n ) triangular numbers, which themselves are formed by the formula ( T_n = \frac{n(n+1)}{2} ). This means a trisquare can be represented as ( S_m = T_1 + T_2 + ... + T_m ), where ( S_m ) is the sum of the first ( m ) triangular numbers. Trisquares have interesting properties in number theory and combinatorics.


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