Question

Last three digits of the number n= 7^100-3^100 are

Answer 1

Given: A number n = 7^100 - 3^100

To find: Last three digit of the given number.

Solution:

• In this question, we have given a number which has a high power and it is time consuming to solve the number.

• Hence we will use the concept of permutation and combination to solve the given number and find the last three digits.

• So, now

               n = 7^100 - 3^100

• It can be written as

               n = (5+2)^100 - (5-2)^100

• Now it can be written as

               n = 2[(100 C 1) x 5^99 x 2 + .............. + (100 C 99) x 5 x 2^99]

• Multiplying 2 inside, we get:

               n = 2[(100 C 1) x 5^97 x 100 + ............... + (100 C 99) x 10 x 2^99]

• Now taking 1000 common, we get

               n = 1000[10 x 5^97 + ............... + 2^99]

• As the number is multiplies by 1000, so lat digits will be 000                

Answer:

           So the last three digits of the number are 000