wu :: forums
        (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi)
      

        riddles >> medium >> A curious divisibility
        
(Message started by: pcbouhid on Nov 25th, 2005, 9:08am)
Title: A curious divisibility
Post by pcbouhid on Nov 25th, 2005, 9:08am
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. Isnīt curious?
Title: Re: A curious divisibility
Post by Barukh on Nov 27th, 2005, 1:46am
[hideb]
1.  26460 = 108 times 245.
2.  108 divides both (27195 – 10887) and  10152.
3.  245 divides both 27195 and (10887 – 10152).
[/hideb]
Title: Re: A curious divisibility
Post by pcbouhid on Nov 28th, 2005, 11:59am
[hide]Simple (after done), isnīt? Good work![/hide]


Powered by YaBB 1 Gold - SP 1.4!
Forum software copyright Đ 2000-2004 Yet another Bulletin Board