Query:Not a Question

Question

I was Going through a question when I came to a conclusion, just wanna verify if its true.

PART I
Suppose n is any digit(0-9), and Given the units digit for n^k is 5,
then for any number(p) that has units digit same as n, 
we have,the units digit for p^k as '5'.
Right?
______________________________________________________________________________________________

PART II
Suppose n is any number and Given the units digit for n^k is 5,
then for any number(p) that has its ending digits same as n, 
we have,the units digit for p^k as '5'.
I am unsure of this.
Please enlighten me.

PS: Reply seperately for Part I and Part II.

Dreaming · Answer

Ummm.......I am quite confused by the round-about logic u have used....but i'll tell u what I know:

for ANY number n ending in 5, n^k will ALWAYS end in 5; provided k is an integer greater than or equal to 1.

Analysis of PART I
Suppose n is any digit(0-9), and Given the units digit for n^k is 5, --> unit digit of n^k will be 5 only for the digit 5 and NO OTHER digit from 0-9. 
then for any number(p) that has units digit same as n,
we have,the units digit for p^k as '5'.
--> this statement doesnt make any sense since the only digit n for which n^k will end in 5 is 5 itself.

same logic applies to Part 2.....only a number n ending in 5 (say 15) will have a n^k form which ends in 5.

vibhav · Answer

Hi Kyro,
The answer to both your parts is the same. All powers of a no. ending in 5 also end in 5. eg. 5^2= 25, 5^4=625 etc. Also no other no has 5 as a units digit in its power cycle. Thus if n^k = xxx5 it means, n will have 5 in its units place. Hope it clarifies.

KarishmaB · Answer

The unit's digit of n^k is decided by only the unit's digit of n.

Part 1: n is any digit and n^k has a unit's digit of say 'a'. Then if p has n as the unit's digit, p^k will also have the unit's digit of 'a'. Only the unit's digit of p decides the unit's digit of p^k
e.g.
 3^4 = 81  (unit's digit 1)

643^4 = ........1  (unit's digit will be 1. When you multiply 643 by 643, the unit's digit is obtained by multiplying 3 by 3 only)

Part 2: n is any number and n^k has unit's digit of 'a'. If p is another number with the same unit's digit as n, then p^k will also have 'a' as the unit's digit.

643^4 = .......1 
 873^4 = ........1

Only unit's digit of n decides the unit's digit of n^k.

Something to think further:
If unit's digit of n^k is 'a' and unit's digit of p^k is also 'a', does it mean the unit's digits of n and p are the same?

Query:Not a Question

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