Don't know where to start when doing these proofs

[jmn_153]

Can anyone please help me with this proof

Prove that every positive integer, ending in 5 creates a number that when squared ends in 25

 

[Hurkyl]

What have you tried?

 

[AKG]

If n is some number that ends in 5, write an equation for n that expresses this fact. If I wanted to say, for example, that n was square, I would write an equation like n = m². If I wanted to express that n was divisible by 14, I would write n = 14k. So what kind of thing should you write to express the fact that n ends in 5?

 

[jmn_153]

yea, Buit I'm not sure what the proper way to start it off is

 

[Hurkyl]

Do you know any way to start it off?

 

[jmn_153]

Would it be n= k + 5

 

[jmn_153]

Or would it be n = 5k

 

[Hurkyl]

Sometimes, one of the first things I do when I have a conjecture is to work out particular examples to see if my conjecture works in those examples.

For your two guesses, I should first ask what you mean by n and k. Next, have you tried particular values to see if it gives you what you want?

 

[jmn_153]

ok, thanks for your help I'll keep trying

 

[AKG]

Posts 6 and 7 are a good start, although one of them will be more useful. Also, in both cases, you'll have to say more about k. For example, if k = 2 then neither k+5 = 7 nor 5k = 10 ends in 5. Note that n = k+5 and n = 5k don't fail for the same k all the time, 2 just happens to be a case where they both fail. k = 3 on the other hand is a case where k+5 fails but 5k works (8 doesn't end in 5, but 15 does). In what cases does k+5 work, i.e. for what values of k? What about 5k? This should tell you what further things you have to say about k. And rather than just saying them about k, work those facts into your expression. For example, if k has to be a perfect cube for n = k+5 to work, then instead write n = k³ + 5, rather than saying, "n = k + 5, where k is a cube."