Question

Check whether (26)n can end with the digit 5 for any n € N

Answer 1

no..according to fundamental theoram of arthimetic, for any number end to the 5 then it should have 0 or 5 in units digit

Answer 2

Answer:

The number $26^n$ cannot end with the digit 5 for any n € N

Solution:

Given number is $26^n$, where n € N

Let us take the value of n be 1, 2, 3, 4, 5, ..

For n=1,

$26 ^ { n } = 26 ^ { 1 } = 26$

For n = 2,

$26 ^ { 2 } = 26 \times 26 = 676$

For n = 3,

$26 ^ { 3 } = 26 \times 26 \times 26 = 17576$

For n = 4,

$26 ^ { 4 } = 26 \times 26 \times 26 \times 26 = 456976$

Hence, we came to know that for any value of n in the given equation $26^n$, the end digit can only be 6 not 5. Thus, it is not possible to have 5 at the end of $26^n$ for any value of n.