Question

If 29 x 77 = 2233 then 0.29 x 7.7 =---- b) If 6.5 divide 1.3 = 5 then 65 divide 1.3=----​

Answer 1

Answer:

As 7 is a prime, by Fermat's little Theorem, 2^7 is congruent to 2(mod 7). Hence 2^50 =[{(2^7)^7}×2] is congruent to (2^7)×2 which in turn congruent to 2×2 = 4(mod 7).

Now 41= (6×7)-1 is congruent to (-1) (mod 7) and hence 41^65 is congruent to (-1)^65 = (-1) i.e. 6(mod 7)