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Topic: Prove 30 divide (ba^5 - ab^5) (Read 640 times) |
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wonderful
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Prove 30 divide (ba^5 - ab^5)
« on: Jun 11th, 2008, 5:16pm » |
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Given a, b are integers, prove that:
30 | (ba^5 - ab^5)
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| « Last Edit: Jun 11th, 2008, 8:24pm by wonderful » |
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Aryabhatta
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Re: Prove 30 divide a^(5b) - b^ (5a)
« Reply #1 on: Jun 11th, 2008, 8:18pm » |
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Something is not right...
a = 2, b =1, we get 30 divides 31...
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wonderful
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Re: Prove 30 divide a^(5b) - b^ (5a)
« Reply #2 on: Jun 11th, 2008, 8:23pm » |
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Thanks Aryabhatta for pointing that out. It should be: 30 | (ba^5 - ab^5). I have revised the original post accordingly.
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Aryabhatta
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Re: Prove 30 divide (ba^5 - ab^5)
« Reply #3 on: Jun 11th, 2008, 8:54pm » |
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Ok.
The following seems to work:
Use the fact that
n5 = n mod 2
n5 = n mod 3
n5 = n mod 5
We see that the given expression is ba - ab mod 2,3 and 5 and hence is divisible by 30.
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wonderful
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Re: Prove 30 divide (ba^5 - ab^5)
« Reply #4 on: Jun 11th, 2008, 8:59pm » |
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Excellent!
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