I'm working on a Koshy's elementary number theory exercise and need help finding all triangular numbers less than 1000 that are palindromic. The problem says as follows: Find all triangular numbers...
Since $1000$ is $1$ mod $3$, we can indeed write it in this form, and indeed $m=667$ works. Therefore there are exactly $1000$ squares between the successive cubes $ (667^2)^3$ and $ (667^2+1)^3$, or between $444889^3$ and $444890^3$.
First of all, from 99 to 1000, we have 100 to 999, meaning $91010$ since 1 to 9 is 9 numbers. We have 900 numbers. Then, to get all numbers with at least one $7$ in their digits, we can do: All
combinatorics - How many numbers are there between 99 and 1000, having ...
The number of bacteria in a culture is 1000 and this number increases by 250% every two hours. How many bacteria is present after 24 hours?
combinatorics - The number of bacteria in a culture is 1000 and this ...
I sat an exam 2 months ago and the question paper contains the problem: Given that there are $168$ primes below $1000$. Then the sum of all primes below 1000 is (a) $11555$ (b) $76127$ (c) $
I found this question asking to find the last two digits of $3^{1000}$ in my professors old notes and review guides. What material must I know to solve problems like this with remainders.I know W...
Solving for the last two digits of a large number $3^ {1000}$?
A hypothetical example: You have a 1/1000 chance of being hit by a bus when crossing the street. However, if you perform the action of crossing the street 1000 times, then your chance of being ...