Let P(n): 5N−5
For n = 1,
p(1): 5-5 = 0 which is divisible by 4.
therefore p(1) is divisible by 4.
Now, suppose p(k) is divisible by 4; k belongs to N.
P(k): 5k−5=4xm; m belongs to N. - - - -- - (1)
Now, we have to prove p(k+1) is divisible by 4.
P(k+1): 5k+1−5
=5k+5−5
=(4xm+5)5−5 <from [1]>
= 5{(4x+5)-1}
= 5{4xm+5-1}
= 5{4x m+4}
= 5{4(m+1)}
=4 (5x m+5) which is divisible by 4
p(k) is divisible by 4 which implies p(k+1) is divisible by 4.
Hence, p(n) is divisible by 4, by PMI