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How many Pythagorean triples are there between 1 and 1,000,000 in which the two shorter sides are separated by 1, aside from the most famous example of 3, 4, 5? Any help would be great. Thank you. 

 Feb 8, 2019
 #1
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Your class must be taking computer programming. This is a job for a simple computer program to figure out. I wrote a short code to search up to 10,000,000 numbers and came up with these:
n= 3^2 + 4^2 = 25
n= 20^2 + 21^2 = 841
n= 119^2 + 120^2 = 28,561
n= 696^2 + 697^2 = 970,225
n= 4,059^2 + 4,060^2 = 32,959,081
n= 23,660^2 + 23,661^2 = 1,119,638,521
n= 137,903^2 + 137,904^2 = 38,034,750,625
n= 803,760^2 + 803,761^2 = 1,292,061,882,721
n= 4,684,659^2 + 4,684,660^2 = 43,892,069,261,881

 Feb 9, 2019
 #2
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Cool!

ElectricPavlov  Feb 9, 2019

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