hi plz solve this...
hi plz solve this
remainder when (5+5^1+5^2+....+5^55) divided by 13
n/a
it can be sum up as
5+ 5(5^55-1)/4
= (15+5^56)/4
so remainder will be
R of (15+5^56)/(4*13)
so final ans is
16
Vandana
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Soln - Pattern method :
5^1| 13 = 5. 5^2| 13 = 12.
5^3| 13 = 8. 5^4| 13 = 1.
5^1| 13 = 5......... Pattern repeats after 4 times.
Original eqn [diving each term individually by 13] = (5+12+8+1)+ (5+12+8+1)+ ........ 13 times + (5+12+8)
= (5+12+8+1) * 13 + (5+12+8) / 13
Rem = 12
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