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The equation for this can be represented as:
n/1261 = m2, where n is our target number and m is an integer
Since there are an infinite number of integers to plug into m, there are an infinite number of perfect squares, which means there are an infinite number of solutions to n.
n = m2 * 1261
The first few solutions could be:
n = 1261, m = 1; (1261)/1261 = 12 = 1
n = 5044, m = 2; (5044)/1261 = 22 = 4
n = 11349, m = 3; (11349)/1261 = 32 = 9
n = 20176, m = 4; (20176)/1261 = 42 = 16
n = 31525, m = 5; (31525)/1261 = 52 = 25
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Is there a product of two perfect squares that is not a perfect square?
No there isn't. every perfect square number can be factored into prime number. At their factoration you'll always have multiples of two on the primes exponent. Therefore you'll multiply a prime raised to a 2-multiple number with another prime raised to a 2-multiple number wich gives you also a number that factored gives you a product of prime numbers raised to a 2-multiple number and so, a perfect square.
Is 80 a perfect square?
Try if you can find an integer that, when squared, gives you 80.
What is the smallest whole number that gives a remainder of 4 when it is divided by 6?
0.6667
What number when divided by four gives and answer of four?
16
What number divided by 32 gives you 4?
128
