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# Undergrad Question help watch

1. Could someone post a solution to this please?
I got as far as showing that the floor function (2+root5)^p - 2^(p+1) is always even.
Attachment 506487506491
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2. (Original post by kprime2)
Could someone post a solution to this please?

Attachment 506487506491
would love to help but I do not do any pure
Most of the purists have left TSR !!
3. (Original post by kprime2)
Could someone post a solution to this please?
I got as far as showing that the floor function (2+root5)^p - 2^(p+1) is always even.
Attachment 506487506491
Write , can you see that this is an integer?

Can you use this combined with the size of (hint:
Spoiler:
Show
negative number close to zero
to show that ?

Now in the two binomial expansions, look at the binomial coefficients, What is this divisible by? So all the terms in the binomial expansions except the first and last term are divisible by that thing. What can you say about the first term, though?

Conclude that .
4. (Original post by Zacken)
Write , can you see that this is an integer?

Can you use this combined with the size of (hint:
Spoiler:
Show
negative number close to zero
to show that ?

Now in the two binomial expansions, look at the binomial coefficients, What is this divisible by? So all the terms in the binomial expansions except the first and last term are divisible by that thing. What can you say about the first term, though?

Conclude that .
Woah wtf haha, I swear you're like an A Level student. Impressive though, shall have another try later.
5. (Original post by kprime2)
Woah wtf haha, I swear you're like an A Level student. Impressive though, shall have another try later.
I made some mistakes that I've edited now.

Edit: tbf so is physicsmaths and you tagged him
6. (Original post by Zacken)
I made some mistakes that I've edited now.

Edit: tbf so is physicsmaths and you tagged him
Haha I meant it as a compliment. What I meant was I'm assuming you're doing STEP or something, as I wouldn't expect an A-level student to tackle a question of that magnitude. But cheers for the help, sounds right.

I swear physmath did like STEP I-III or some **** so I thought he'd knew. :P
7. (Original post by kprime2)
Haha I meant it as a compliment. What I meant was I'm assuming you're doing STEP or something, as I wouldn't expect an A-level student to tackle a question of that magnitude. But cheers for the help, sounds right.

I swear physmath did like STEP I-III or some **** so I thought he'd knew. :P
I did take it as a compliment! Yeah, I've got a Cambridge offer, so I'll be doing STEP I-III as well.
8. (Original post by Zacken)
I did take it as a compliment! Yeah, I've got a Cambridge offer, so I'll be doing STEP I-III as well.
Amazing. Well done!
9. (Original post by kprime2)
Amazing. Well done!
Thanks.

Let me know how you get on with the question and whether my approach works or not.

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