what is the remeinder of ((25)^625 + 26)/247...???? kan ne1 help me !!! i saw its solution on this site only but i m not able to understand can anyone of you explain in detail............ please help me out.
25^625=5^1250 247=19*13....the E.N. for this is 216 hence, 5^1080%247=1 thus, we need to find the remainder when 5^170/(19*13) applyin chinese remainder thm.... we need an x such that x=12%13 x=4%19 solvin we get, x=38+403=441 i.e.x=441-247=194 so, for the 1st part, the rem is 194.... for the nxt part it is 26 hence, the ans:194+26=220
@ shivanibusiness hi i understand your approch till euler theorem but after that this chinese remainder theorem is nt clear to me can you please explain how you applied this .............plz explain it to me
This is the way i did it....
((25^625)+26)/247 = [{25^624}*25)+26]/247
=(((64^208)*25)+26)/247 (as 25^3/247 leaves a remainder of 64)
=(((4^624)*25)+26)/247 (as 4^3 = 64)
=(((9^156)*25)+26)/247 (as 4^4/247 leaves a remainder of 9)
=(((3^312)*25)+26)/247 (as 3^2 = 9)
=(((3^310)*9*25)+26)/247
=(((-4^62)*9*25)+26)/247 (as 3^5/247 leaves a remainder of -4)
=(((16^31)*9*25)+26)/247 (as -4^2= 16)
=(((16^30)*16*9*25)+26)/247
=(((9^15)*16*9*25)+26)/247 (as 16^2/247 leaves a remainder of 9)
=(((3^30)*16*9*25)+26)/247 (as 3^2 = 9)
=(((-4^6)*16*9*25)+26)/247 (as 3^5/247 leaves a remainder of -4)
=(((16^3)*16*9*25)+26)/247 (as -4^2= 16)
=(((16^4)*9*25)+26)/247
=(((9^2)*9*25)+26)/247 (as 16^2/247 leaves a remainder of 9)
=(((9^3)*25)+26)/247
=(((3^6)*25)+26)/247 (as 3^2 = 9)
=(((3^5)*3*25)+26)/247
=(((-4)*3*25)+26)/247 (as 3^5/247 leaves a remainder of -4)
=((-300)+26)/247
=(-274)/247
=(-247-27)/247
thus the remainder is (-27) or +220
get it......
25^625=5^1250
247=19*13....the E.N. for this is 216
hence, 5^1080%247=1
thus, we need to find the remainder when 5^170/(19*13)
applyin chinese remainder thm....
we need an x such that
x=12%13
x=4%19
solvin we get, x=38+403=441
i.e.x=441-247=194
so, for the 1st part, the rem is 194....
for the nxt part it is 26
hence, the ans:194+26=220
n/a
@ shivanibusiness
hi
i understand your approch till euler theorem but after that this chinese remainder theorem is nt clear to me can you please explain how you applied this .............plz explain it to me
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