# Math Contest #14 Results and Solution

## Solution

The problem of this contest was again a set of 2 equations:

Apart from the obvious solution `(0, 0, 0)` there is also an infinite number of other solutions:
1: `x² + y² = z²`
2: `z = x² + y``x² = z - y`
x² in 1: `y² - y + z = z²``y² - y + z -z² = 0`
→ 3:`y = ½ ± √(¼ + z² - z)`
`(z-½)² = z² -z + ¼` in 3: `y = ½ ± (z - ½)`
→ Either y = z(this leads to x = 0) or y = 1-z:
y in 2: `z = x² + 1 - z``x² + 1 = 2z`
For z to be an integer x² and therefor x need to be odd:
x = 2n + 1, n is any integer.
→ z = 2n² + 2n + 1
→ y = -2n² - 2n
So the solutions are:
`(0, n, n)`, `(2n + 1, -2n²-2n, 2n²+2n+1)`, n is any integer.
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### What is your chance of winning:

`p(You Win) = 1/n`, `n = number of entries`

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### List of participants with their entries:

Name solutions found comment
@tonimontana Only one of the general solutions You found the trivial case of y=z, but not the general case.

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## Winner draw:

not needed

Congratulations @tonimontana, you won 1 SBI!
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### The next contest starts tomorrow. Don't miss it!

Hi @quantumdeveloper, a small upvote and a tip.
\$trendotoken

04.10.2019 10:51
2

Congratulations @addax, you are successfuly trended the post that shared by @quantumdeveloper!
@quantumdeveloper got 0.14652000 TRDO & @addax got 0.09768000 TRDO!

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04.10.2019 10:51
0

Thanks!

04.10.2019 13:36
8