51/7=2 remainder i.e. 2 to the power 203..again 2 to the power 3 * 2 to the power 200 which again if divided by 7 i.e. 2 to the power 3 divided by 7 will give remainder 1...so, final answer 1...isnt it a correct ans??...kindly xplain...thnks in advance... CHEERS!!
i dint quite get what u meant?? thoda numbers leke explain karoge?
Hi everyone! Find the remainder when 55^190 is divided by 153? The answer key says 120 but I'm getting 118 as the answer. Where did I go wrong
153=17*9
55%9=1
so rem will be of the form 9k+1. 118 hi hoga bhai. 120 isnt fitting. u r correct.
@Godschild : Thanks for the link :) Find the total number of natural numbers n for which 111 divides (16^n)-1, Where n is less than 1000.
111 = 37 * 3
mod3 = 0 (for all n)
E = 36
So 16^36mod37 = 1 Now we need to check if there is a lower power of 16 other than 36 that gives the remainder 1 when divided by 37. So we check for factors of 36 as possible powers.
The number of positive integers valued pairs (x, y) satisfying 4x - 17y = 1 and x (1) 59 (2) 57 (3) 55 (4) 58 Please explain the answer. I am getting 58.
It should be 59.
4x-17y = 1 => 4x = 17y+1 => 4x = 16y + y + 1 It means, when y leaves remainder by 4 as 3, 17y+1 is divisible by 4. So, y can be 3, 7, .... Now, 4000/17 = 235.xx So, maximum values y can take = 236/4 = 59
The number of positive integers valued pairs (x, y) satisfying 4x - 17y = 1 and x (1) 59 (2) 57 (3) 55 (4) 58
Please explain the answer. I am getting 58.
My method:
y = (4x - 1)/17
Now, 1000/17 gives 58 and 14 remainder.
I m gtng 59 as my ans...as 1st pair which satisfies the above eq vl be(13,3)...now adding (17,4) we will get next pair and thus a total of 59 pairs ..last being(999,235).
