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yup thats the correct approach and thats what i wanted to explinpradeepkaushal9518 wrote:i have simply done 17 divide by 16 gives remainder 1 for 23 numbers of 17 will give reaminder 1.
is this true for all this type of questions
could u explin in more detail how it works? how are u calculating these mods?nathanalgren wrote:Guys, if you know what modular arithmetic is, this is the easiest and fastest way to solve these kind of questions.
17^1 = 1 (mod 16)
So any power of 17 = 1 (mod 16)
This could be implied to any kind of remainder questions. The other approaches written here are okay, but this is far best.
Another example: Suppose it asked the remainder of 18^34 divided by 13.
18^1=5 (mod 13)
18^2=12 (mod 13)
18^3=8 (mod 13)
18^4=1 (mod 13)
The remainder of 34/4 is 2. So we look at 18^2=12 (mod 13).
Hence the remainder of 18^34 divided by 13 is equal to 12.
Yup !! It works and thanks for making me understand this concept.amising6 wrote: You will get 2*2*2*2*..23 times(if I have correctly understood your point) ...then how will you proceed from here...??
now make a group of four 2's i.e 16 *16*16*16*16*8 divide by 15
so every 16 will give 1so u will be left with 1*8 mod 15=8
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