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You can generate Pythagorean triples using Euclid’s formula:
a = m^2 – n^2
b = 2mn
c = m^2 + n^2But the key thing to note here is a = m^2 – n^2 = (m – n) (m + n). So given any odd positive integer (except 1), we can force m – n = 1 and so a = m + n. For example for 23, we can make m = 12 and n = 11, and so a = (12 – 11) (12 + 11) = 23. Therefore the other 2 integers are b = 2mn = 2 * 12 * 11 = 264 and c = m^2 + n^2 = 12^2 + 11^2 = 265.
In summary given a odd integer k, we can find the 2 other integers, b and c, such that k, b, c make a Pythogorean triangle:
b = (k + 1) (k – 1) / 2
c = ((m + 1)^2 + (m – 1)^2) / 4This answer accepted by ronret45. on 5th March 2016 Earned 20 points.
- 4975 views
- 1 answers
- 1 votes
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It’s only 19. You probably counted 88 twice
- 7707 views
- 4 answers
- 0 votes
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When the day after tomorrow is yesterday = 4 days from now
When the day before yesterday was tomorrow = 4 days agoReplacing the values of today with the appropriate when:
4 days from now will be as far from Wednesday, as 4 days ago was from Wednesday.This is only true when today is Wednesday. So tomorrow is Thursday.
- 4776 views
- 2 answers
- 0 votes
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x = 0.25 * 5 + 0.25 (x + 8) + 0.25 * 3 + 0.25 (x + 2)
x = 1.25 + 0.25x + 2 + 0.75 + 0.25x + 0.5
x = 4.5 + 0.5x
0.5x = 4.5
x = 9- 5601 views
- 1 answers
- 0 votes
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February, because there are less days
- 6603 views
- 2 answers
- 0 votes