Prime or composite?

OP

UCASquestions

You know you're a virgin when you attempt the Oxford Mathematics puzzle of the day...

Well, I know of it because I work at the Oxford Centre For Nonlinear PDE (and I got laid [twice] this morning, not that it matters :p:

).

Reply 3

UCASquestions

Dream Eater

Well, I know of it because I work at the Oxford Centre For Nonlinear PDE (and I got laid [twice] this morning, not that it matters :p:

).

, too much info. :rofl2:

Reply 4

∏ Squared Over 6

Dream Eater

Is the number

\displaystyle \frac{2^{58} + 1}{5}

prime or composite?

[Ripped from the Oxford Maths Institute puzzle of the day, so one would assume 5 is a factor of the numerator. I am genuinely interested in how others might go about solving this... I am having some trouble.]

EDIT: For completeness http://www.maths.ox.ac.uk/noticeboard/last_puzzle

My first thoughts are:

Spoiler

Not sure if this is going anywhere! :smile:

And yeah too much info there :smile:

Reply 5

composite.

mini hint

Spoiler

massive hint

Spoiler

Reply 6

Zhen Lin

12

Dream Eater

Is the number

\displaystyle \frac{2^{58} + 1}{5}

prime or composite?

[Ripped from the Oxford Maths Institute puzzle of the day, so one would assume 5 is a factor of the numerator. I am genuinely interested in how others might go about solving this... I am having some trouble.]

EDIT: For completeness http://www.maths.ox.ac.uk/noticeboard/last_puzzle

2^{58} + 1 \equiv 2^2 + 1 \equiv 0 \pmod 5

, so the numerator is indeed divisible by 5. Alternatively, note that

x^{58} + 1 = (x^2 + 1)(x^{56} - x^{54} + \cdots + 1)

.

Beyond that, I have no idea.

Reply 7

Dream Eater

Well, I know of it because I work at the Oxford Centre For Nonlinear PDE (and I got laid [twice] this morning, not that it matters :p:

).

was it good sex though? that's what we all want to know.

Reply 8

UCASquestions

Totally Tom

was it good sex though? that's what we all want to know.

, aahhaahahahha. :rofl3:

Reply 9

OP

Totally Tom

massive hint

2^{58}+1=(2^{29}+1)^2-2^{30}

now think difference of 2 squares...

Yay! I thought it involved Fermat's Factorisation method but I couldn't think of where to apply it. Cheers :smile:

Reply 10

OP

Totally Tom

was it good sex though? that's what we all want to know.

Bloody fantastic. Had tea afterwards and everything.

Reply 11

Dream Eater

Bloody fantastic. Had tea afterwards and everything.

:hi5:

Reply 12

Dream Eater

Yay! I thought it involved Fermat's Factorisation method but I couldn't think of where to apply it. Cheers :smile:

try this one:

is

\displaystyle\frac{3^{76}+4}{5}

prime or composite?

using a different method to before (unfortunately the other method works here too).

Reply 13