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1d
revised Assume that the sum of absolute values of all entries of $A$ equals to $1$. What is the maximal possible value of $\det(A)$?
added 11 characters in body
1d
answered Assume that the sum of absolute values of all entries of $A$ equals to $1$. What is the maximal possible value of $\det(A)$?
May
7
comment Show that $f(a)$ converges after some point
@Amad27For the first hint. If $a_1, s_2$ are the same, then so must $f(a_1), f(a_2)$. This tells us that the number of distinct integers cannot increase. It might decrease, like in Henry's example above.
May
6
comment Show that $f(a)$ converges after some point
@Amad27 That does not matter. Which hint are you stuck at? Can you prove the first hint? Can you prove the second hint?
May
4
revised Show that $f(a)$ converges after some point
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May
4
revised Show that $f(a)$ converges after some point
deleted 39 characters in body
May
4
answered Show that $f(a)$ converges after some point
Apr
28
comment Why is $2(5u_p)^2\equiv (1+5^p)+4 \bmod 2p-1$?
Can you check, For $p=2$, $LHS =5$, $RHS = \frac{1}{8} ( 1 + 6\times 5 + 5^2) + 2 = 7 + 2 = 9 $.
Apr
16
comment Simplifying Sum
Did you try inducting on $n$ and $m$?
Mar
27
awarded  Peer Pressure
Mar
24
answered Fake induction proofs
Mar
24
answered Need help with a determinant proof.
Mar
24
answered A sequence 〈a_n〉 is defined recursively ,and find infinite series
Mar
24
answered Does $\lambda_1^n+ \lambda_2^n+ \dots +\lambda_k^n =0 $ for all $n$ imply that $\lambda_1= \lambda_2= \dots= \lambda_k = 0 $?
Mar
24
comment INMO Problem with even function proof.
@barto Isn't a "can I have hint" question very different from a "Give me the answer" question? Or does MSE consider these duplicates of each other?
Mar
24
comment AMC $12A$ Problem (Sequence lengths)
@GeoffreyCritzer Yes, every recurrence relation will eventually repeat modulo any number $n$. Proof: If it is recurrence on $k$ terms, consider the first $n^k+k$ terms mod $n$. There must be some string of $k$ of them which are identical. From this string, by the linear recurrence, each subsequent term is identical. Note: It is much faster to apply Chinese Remainder Theorem and work on this mod 3 and mod 4 separately (then to figure out the period is 52).
Mar
23
comment AMC $12A$ Problem (Sequence lengths)
@GeoffreyCritzer Note you we only need the answer mod 12. So, simply list it out mod 12, and find out the period.
Mar
22
awarded  Sportsmanship
Mar
22
revised INMO Problem with even function proof.
added 225 characters in body
Mar
22
comment INMO Problem with even function proof.
Well, use the fact that $ (n+1) - n $ = 1 to conclude that if $ n < ik \leq n+1 $, then we must have $ik = n+1$, or that $k$ divides $n+1$.