binomial

although i was able to get the ans by congruence modulo... any idea how to do this by binomial theorem? i tried by writing them as 19+4 and 19-4 but did not get anything useful
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@Apu
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SirLancelotDuLac
Consider division by 19, there's no remainder by binomial. Now consider 3 and write 23 as (24-1)
vj25_
vj25_OP2mo ago
how do i approach this using binomial tho i did the exact same thing while using congruence
vj25_
vj25_OP2mo ago
tried by this way for binomial
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vj25_
vj25_OP2mo ago
forgot to multiply 4^2 in third and fourth line second term mb
SirLancelotDuLac
After this, if you wanna do this way, write out 19 everywhere to 18+1, then you get a double summation kinda thingy Solve that to get some k.2^m kinda stuff After that write it out as k.(3-1)^m After which you get the remainder. So yea...using 19 and 3 is better
vj25_
vj25_OP2mo ago
yeahh my method is really messy 19 and 3 se sahi se ho ja rha hai thankss +solved @SirLancelotDuLac
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