Question

Prove the divisibility of the following numbers:

25^9 + 5^7 is divisible by 30.

Also, read as (25 to the power of 9) + (5 to the power of 7) is divisible by 30.

Answer: Blank x 30
What is the blank? ( It should be expressed in exponent form)

Answer 1

Explanation:

prove : 25^9 + 5^7 ≡ 0 ( mod 30) or 5^18 + 5^7 ≡ 0 ( mod 30)

because : 25= 5²

calculate 5^p for 1 ; 2;3 ; 4....

5^1 ≡ 5 ( mod 30)

5^2 ≡ 25 ( mod 30)

5^3 ≡ 5 ( mod 30)

5^4 ≡ 25 ( mod 30)

p = 2k+1 5^p ≡ 5 ( mod 30)

p = 2k 5^p ≡ 25 ( mod 30)

so : 5^18 ≡ 25 ( mod 30) ......(*)

5^7 ≡ 5 ( mod 30)...........(**)

add (*) and (**) :5^18 + 5^7 ≡ 0 ( mod 30) because : 30≡0 (mod30)