AS paper: Prove every prime > 5, when raised to 4th power, ends in 1

Sean123

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Hi, there was this question on my AS maths paper and me and my class cannot agree on how to answer it... it went like this.

Prove that every prime number above 5 when raised to the power of 4 will always end in a 1

n is a prime number
So prove n^4 always ends in a 1

If anyone can prove that to me then thankyou. In my exam in a panic I attempted proof by exhaustion but that wont work since there is no range given.
 
Hi, there was this question on my AS maths paper and me and my class cannot agree on how to answer it... it went like this.

Prove that every prime number above 5 when raised to the power of 4 will always end in a 1

n is a prime number
So prove n^4 always ends in a 1

If anyone can prove that to me then thankyou. In my exam in a panic I attempted proof by exhaustion but that wont work since there is no range given.

I prime number above 5, cannot have 2, 4, 6, 8 or 0 at the unit digit.

It cannot have 5 either.

Now what.....
 
Problem can be worded this way:
prove that all numbers ending with 1,3,7 or 9
to the power 4 end with 1.
1^4 = 1
3^4 = 81
7^4 = 2401
9^4 = 6561

Done!
Magnifique, mon ami!

And any number ending with an even digit to the fourth power ends in an even number and any number ending with 5 to the fourth power ends in 5.
 
Last edited:
Magnifique, mon ami!

And any number ending with an even digit to the fourth power ends in an even number and any number ending with 5 to the fourth power ends in 5.
Oh, I guess you do not know. If you complement Denis it really goes to his head. It takes him weeks to recover. Is it too late to delete the post?

Have a great night!
 
Problem can be worded this way:
prove that all numbers ending with 1,3,7 or 9
to the power 4 end with 1.
1^4 = 1
3^4 = 81
7^4 = 2401
9^4 = 6561

Done!
I suggest we should let the OP discover the answer with nudge and help. Denis - you are trying to be new Soroban.......
 
Problem can be worded this way:
prove that all numbers ending with 1,3,7 or 9
to the power 4 end with 1.
1^4 = 1
3^4 = 81
7^4 = 2401
9^4 = 6561

Done!

Thank you, you are correct however the question was asking for algebraic proof so listing 4 examples, although they work, doesnt prove it for every value possible
 
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