Can a Graduate Degree from Oxford U help me get a salaried position in trading?

[candletrader]

Quote from nitro:

For what primes p, is 2^p + p - 1 = x^2?

Note that 5 works: 2 ^5 + 5 - 1 = 6 ^2.

Is five the only prime? Are there an infinite number of them? Please show me how you would go about solving this problem - the answer is not important, just how you would attack it.

nitro

Hehe, Brother nitro.... interesting problem...

 

[nitro]

Quote from TGregg:

X is always an int?

Yes, this is a Number Theory problem (Mathematicians call the Integers, Z, for Zahlen, a German word.)

However, remember for example, when factoring x^2 - 1 = y, y in Z, the left hand side becomes (x+1)(x-1) = y. That is, x is still in Z. However, factoring x^2 + 1 requires the Gaussian Integers Z, i.e., x^2 + 1 is not factorable in Z, but in Z, ( x + sqrt(-1) ) ( x - sqrt(-1) ) = y. If you expand and collect the left hand side, you will see that it equals x + 1.

nitro

 

[cartm]

That was fun.