Official TSR Mathematical Society

Find all integer solutions of $y^2 = x^3 - 432$.

PRSOM
Is that really a quotable result?

In the case of n = 3 (and some other ones) it's elementary to prove. (Not easy though IIRC)

This is a special collection of problems that were given to select applicants during oral entrance exams to the math department of Moscow State University. These problems were designed to prevent Jews and other undesirables from getting a passing grade. Among problems that were used by the department to blackball unwanted candidate students, these problems are distinguished by having a simple solution that is difficult to find. Using problems with a simple solution protected the administration from extra complaints and appeals. This collection therefore has mathematical as well as historical value.

Copy-pasted from reddit, but this is ridiculously cool:

http://imgur.com/c480O

It is well known that the harmonic series, 1/1 + 1/2 + 1/3 + 1/4 + ... , diverges. Consider a depleted harmonic series; see below; which contains only terms whose denominator does not contain a 9. (In decimal representation.) Does this series diverge or converge?

S = 1/1 + 1/2 + ... + 1/8 + 1/10 + ... + 1/18 + 1/20 + ... + 1/88 + 1/100 + 1/101 + ...

Standard analysis question?
Interesting none the less.

It is well known that the harmonic series, 1/1 + 1/2 + 1/3 + 1/4 + ... , diverges. Consider a depleted harmonic series; see below; which contains only terms whose denominator does not contain a 9. (In decimal representation.) Does this series diverge or converge?

S = 1/1 + 1/2 + ... + 1/8 + 1/10 + ... + 1/18 + 1/20 + ... + 1/88 + 1/100 + 1/101 + ...

Standard analysis question?
Interesting none the less.

Converges.

1st year analysis problem sheet so I guess standard. IIRC counting digits and bounding the sum is the entire proof.

At the same time we had an interesting prob question on the R-Z function.

1/zeta(s) = product(1 - (1/p^s)) product over p prime.

Suggestion - consider Y the probability a number x is divisible by p. Show Y and p prime are independent (also complements). Look at the intersection of primes not dividing X.

I'm failing to see an actual question. Solve for p or s? prove it?

prove 1/zeta(s) = product over p prime (1 - 1/p^s) via probability.

The lecturer teaches the 1st years in 3 weeks so he has not put the question sheet up. It would have been worded better (and I've had to do this question roughly 10 times in the past year so I'm not doing it again in order to reword the question).

prove 1/zeta(s) = product over p prime (1 - 1/p^s) via probability.

The lecturer teaches the 1st years in 3 weeks so he has not put the question sheet up. It would have been worded better (and I've had to do this question roughly 10 times in the past year so I'm not doing it again in order to reword the question).