Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

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
11 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

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free