New challenge:

All we hv to do is to prove that 9k^2 - 1 is divisible by 8.

=(3k+1)(3k-1) this reduces down to your other question -- product of 2 consecutive even nos is div by 8.......

New challenge:

]]>Next one?

]]>Induction proves the second pretty quickly:

Obviously the first part could also be done (and more quickly) by induction, but I feel induction gets rid of the 'why' behind it. I'm sure you're going to show me a nicer way to do the second part

]]>P = 4A

T = 1.5P

P+A+T=47

From here it is straightforward to solve.

]]>If Peter is 4 times the age of Adam and Tom is ½ more than the age of Peter and the total sum of their ages is 47 then how old will each boy be?

TELL ME IF IT MAKES SENSE LOL

It would be helpful if we could multiply by a number n such that 13n is 1 more than a mutliple of 29. The smallest such number is 9. Mutliplying by 9 gives:

i.e.

Thank you Jane

]]>Very well, heres a simple question for you.

Find all integer solutions

to the congruence equationThe solution uses material you should be familiar with (because Ive seen you discuss it on the forum). Let me know if you need a hint.

]]>By challenging questions I mean ones which require insight and clever tricks, or ones with nice results, rather than something that requires a lot of knowledge and can be done by appyling heavy theorems.

Content-wise they can contain anything that doesn't assume too much university-level knowledge, although I would like to learn some things along the way so don't hold back.

I'm mainly looking at people like Jane, mathsy and Ricky, but anyone else is of course welcome

Thank you.

]]>