Question 1029872
We are given that the hypotenuse of a right triangle is 37 and
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a^2 + b^2 = 37^2 = 1369
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37 is a prime of the form (4k+1) and 1369's prime factorization is 37^2
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If a whole number's prime factorization has primes only of the form (4k+1), then it can be written as the sum of two squares
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From the definition of a triangle, we know that
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a + b > 37
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Consider perfect squares less than 1369
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1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289,
324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961,
1024, 1089, 1156, 1225, 1296
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12 and 35 are the only pair of integers that satisfy the following
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12^2 + 35^2 = 1369
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