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A square whose side length is a triangular number can be partitioned into squares and half-squares whose areas add to cubes. From Gulley (2010).The n th coloured region shows n squares of dimension n by n (the rectangle is 1 evenly divided square), hence the area of the n th region is n times n × n.
Perfect square dissection, a dissection of a geometric square into smaller squares, all of different sizes Perfect square trinomials , a method of factoring polynomials Topics referred to by the same term
Consequently, a square number is also triangular if and only if + is square, that is, there are numbers and such that =. This is an instance of the Pell equation x 2 − n y 2 = 1 {\displaystyle x^{2}-ny^{2}=1} with n = 8 {\displaystyle n=8} .
289 is a perfect square being equal to 17². It is also the 7th number to only have 3 factors because it is a square of a prime number. 289 is the sum of perfect cubes. It is the sum of 1³+2³+4³+6³. 289 is equivalent to the sum of the first 5 whole numbers to their respective powers. It is equal to 0⁰+1¹+2²+3³+4⁴.
A square-free integer is an integer that is not divisible by any square other than 1. square number A square number is an integer that is the square of an integer. For example, 4 and 9 are squares, but 10 is not a square. Szpiro Szpiro's conjecture is, in a modified form, equivalent to the abc conjecture.
WASHINGTON (Reuters) -A U.S. Justice Department watchdog report released on Thursday debunked claims by far-right conspiracy theorists who falsely alleged that FBI operatives were secretly ...