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pcbouhid
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A curious divisibility  
« on: Nov 25th, 2005, 9:08am »		 Quote Quote Modify Modify
Without evaluation of it, prove that the number N = 27,195^8 - 10,887^8 + 10,152^8 is divisible by 26,460.
 
Note that 27,195 - 10,887 + 10,152 = 26,460. Isn´t curious?
 
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Barukh
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Re: A curious divisibility  
« Reply #1 on: Nov 27th, 2005, 1:46am »		 Quote Quote Modify Modify
hidden:

1.  26460 = 108 times 245.
2.  108 divides both (27195 – 10887) and  10152.
3.  245 divides both 27195 and (10887 – 10152).

 
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pcbouhid
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Re: A curious divisibility  
« Reply #2 on: Nov 28th, 2005, 11:59am »		 Quote Quote Modify Modify
Simple (after done), isn´t? Good work!
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