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...2 are arranged such that m is in the ceiling(m/n) row and the (m-1)(mod n)+1 column.
Take the n=4 grid of positive integers:
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
Try to find a permutatio...
I call a set P of positive integers primeary if the sum of an odd number of elements of P is always prime.
It's clear what the sum of an odd number k > 1 of integers means; for k = 1, the sum of an
... is congruent to 1 mod 3. Therefore 10 to the power N is congruent to 1 to the power N, which is 1, for any positive integer N.
Therefore a googol = 10^100 is congruent to 1 mod 3. A googolplex has ...
Start with an n-by-n grid. Place n^2 positive integers into the grid such that: Each integer is greater than the integer placed previously. Each integer is left of, right of, below, or above the integ
...ual and the other question to a different individual).
What two questions would you ask so that you would positively find heaven? NOTE: A question cannot be asked which will cause the respondent to ...
...an n-by-n grid drawn on paper. (I suggest an n of at least 5.)
Before play each player *secretly* picks a positive integer.
Starting in the upper left square, players take turns filling in one squ...
...add lowest prime > n 4) add or subtract 1 5) multiply by highest prime dividing n 6) subtract the number of positive divisors of n 7) if (n+1) is composite then dead-end. 8) divide by highest prime di...
...es the mean absolute (or mean squared) difference between sum(h_i x_i) and sum (h_i p_i) for a given set of positive weights h_i. It seems there should be a slick, easy way to do this, no?
The motiv...
...Now, as intended here, I am referring to the finite number of elements which are in the database.
(So, = positive integers (...
...after several false solutions, I have finally given up.
What is the number of permutations of the first m positive integers where
GCD(a(k-1), a(k)) = 1
for all k, 2 ...
Why is a negative number, multiplied or divided by another negative number, result in a positive solution?
There is really no real world application to this theory. Look at the following 'laws of ma
...rfect square for m = 1 and m = 3 (at which it takes the values 3^2 and 17^2, respectively). Are there other positive integer values of m which make F(m) a perfect square? If not, can you prove your as...
This seems like something that MUST have been thought about before.
For a positive integer, n, take all of the distinct integers 1 to n. Place them along an integer number-line such that: (Or you ca
Unless there is a pure-math proof of a solution/non-solution, this is a kind of math-based maze.
For a positive integer n, take an n-by-n grid. Label the rows with the first n primes, and do the sam
Begin with a finite set of integers (such as all the positive integers
Let q and r be NONNEGATIVE integers. Let m be a positive integer.
Let:
Prove product of any N consecutive positive integers is divisible by N! ( N factorial).
...sure that there are 6 magic squares that can be constructed from the integers of 1 to (6 *n^2), for all n = positive integer.)
Thanks, Leroy Quet...
Let a(0,m) = 1 (for every positive integer m).
For n = nonnegative integers, m = positive integers,
let a(n+1,m) =
m * sum a(n,k) binomial(m+n,k+n) (-1)^(k+1) /k.
In ascii-art mode:
a(n+1,m)
prove or disprove: does there exist a positive integer N such that there exist integers r, s, t where N = r^2 + 1 = s^3 + 1 = t^5 +1. If so find the smallest such N and prove it is minimal.
4 can be expressed by these 8 sums of positive integers: 4, 1+3, 2+2, 3+1, 1+1+2, 1+2+1, 2+1+1, 1+1+1+1. How would you prove that a positive integer N can be expressed by 2^(N-1) sums of positive inte
...e it is not as simple as that, for a hole could mean more than one different things, e.g. a hole that is a 'positive ion' with a relative lack of electron(s), or a hole that is an 'explicit lack of on...
...ce the statement 'Any n people in Central Park at the same time all have the same birthday' is true for all positive integer values of n.
Isn't it?...
... SM3 = 123 SM4 = 1234 ... SM10 = 12345678910 SM11 = 1234567891011 etc.
a) Find n such that n is the least positive integer >= 1000
where 7 is a prime factor of SMn.
b) Find n such that n is the ...
...achievement of someone who had never done anything particularly impressive prior to age 35? I'm looking for positive achievemnets here, no Darwin awards please....
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