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Show that 19 93 -13 99 is a positive integer divisible by 162.

Show that 1993-1399 is a positive integer divisible by 162.

Grade:Upto college level

1 Answers

askiitianexpert arulmani
6 Points
14 years ago
Both 19^93 and 13^99 are odd, so odd – odd is even and is divisible by 2, so it’s enough we need to show that 19^93 and 13^99 is divisible by (162 / 2) which is 81. Now, 19^93 (modulo 81) = (18 + 1)^93 (modulo 81) = 93(18) + 1 = 55 (modulo 81) Similarly, 13^99 (modulo 81) = (12 + 1)^99 (modulo 81) = 99(12) + 1 = 1189 (modulo 81) = 55 (modulo 81) Hence, 19^93 – 13^99 = 0 (modulo 81) Therefore, 19^93 and 13^99 is divisible by 162

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