Prove that 3^(2n+1)+2^(n+2) is divisible by 7

Please give me a detailed explanation

Prove that 3^(2n+1)+2^(n+2) is divisible by 7

Prove that 9^n-8^n is divisible by 8

Find the no of zeros at the end of 100!?

Please give a detailed explanation

State and prove the test of divisibility of a positive integer ‘a’ by 11.

Oh, the diameter of the semicircle lies on the line AC

1. If real numbers x,y,z satisfy (x^2/y^2)+(y^2/z^2)+(z^2/x^2)=x/y+y/z+z/x, then prove that x=y=z
   
    

p is a prime, n a positive integer and n+p =2000. LCM of n and p is 21879. Then ______________ and                .

In a triangle ABC, AB = 12, BC = 18, CA = 25. A semicircle is inscribed in D ABC such that the diameter of the semicircle lies on . If O is the centre of teh circle, then the length AO = ___

4)If u observe carefully there is a repetition in the units digit the powers of each one:

17^1=7 

17^2=9

17^3=3

17^4=1

Therefore in 17 there is a repetition in the units digit,for an incease of 4 in the power the units digit repeats:

Therefore units digit of 17^2005=2005/4 reminder is 1

the units digit is the units digit of 17^1 i.e 7

7 also follows that pattern therefore the units digit of 7^2005 is 7

The units digit of all the powers of 11 is 1

Therefore units digit is

7+1-7=1

Therefore units digit is 1