Thread: question involving modulus (congrency)

Hi

I need help with the following question

I have attached my question.

I haven't got a clue on how to start the question.

thanks

Originally Posted by cooltowns

Hi

I need help with the following question

I have attached my question.

I haven't got a clue on how to start the question.

thanks

First, you prove that any integer to the 4th power is 0,1,2,or 4 mod 7, and then you reduce the given question modulo 7 and get that there's no solution to it and thus there's no integere solution for it, either.

Tonio

can you please show me how to do it, i would appreichate this. I have a few questions which are similar to this. So if i have fully worked out solution to one i can try others on my own.

thanks

You solve it by doing it! What is ? What is ? What is ? What is ? What is ? What is ? What is What is ?

Now reduce "(mod 7)". Since 7= 0 (mod 7) that reduces to (mod 7). Is there any integer y for which that is true? Replace with 0, 1, 2, and 4 to see.

could you please explain how the

i don't understand where the 2 came from and why you have chosen mod7 in particular.

thanks

Obviously:



Now we know that

So what are the possible values of and are any of these congruent to

CB

but why 2(mod7). As i understand the mod 7 comes from the equation but could you please explain where the 2 came from ?

thank you

Originally Posted by cooltowns

but why 2(mod7). As i understand the mod 7 comes from the equation but could you please explain where the 2 came from ?

thank you

It's the right hand side of your d**n problem:



There is a bit of a hint also in the question that is involved.

To prove that an equation has no integer solutions it is sufficient to show that it has no solution modulo some integer.

(As a hint in future read your own problem when you post it)

CB

thanks for all the replies.