Search found 138 matches
- Fri Jun 08, 2012 11:19 am
- Forum: Secondary Level
- Topic: Solve it!
- Replies: 5
- Views: 4444
Answer
x=0 and y=0
- Sun Apr 15, 2012 11:10 pm
- Forum: Secondary Level
- Topic: Find The Remainder
- Replies: 2
- Views: 2380
Find The Remainder
What will be the remainder if you divide $72^{1001}$ by $31$ ?
- Sun Apr 15, 2012 1:53 pm
- Forum: Junior Level
- Topic: No repeated digits: 100-999
- Replies: 8
- Views: 6227
No repeated digits: 100-999
How many 3 digit positive integers have no repeated digits.
- Sun Apr 15, 2012 1:44 pm
- Forum: Secondary Level
- Topic: Primes
- Replies: 4
- Views: 3153
Primes
Prove that if p and \[p^{2}+8\] both are prime, then \[p^{3}+4\] is also prime.
- Sun Mar 25, 2012 12:25 pm
- Forum: Secondary Level
- Topic: DUET math olympiad 2012
- Replies: 4
- Views: 3924
Re: DUET math olympiad 2012
\[3^{a}=36\] \[\Rightarrow log3^{a} = log 36\] \[\Rightarrow a log3 = log 36\] \[\Rightarrow a = \frac{log 36}{log 3}\] Similarly, \ Now \[\frac{2}{a} + \frac{1}{b}\] \[\frac{2}{\frac{log36}{log3}} + \frac{1}{\frac{log36}{log4}}\] \[\frac{2log3}{log36} + \frac{log4}{log36}\] \[\frac{2log3+log4}{log3...
- Tue Mar 06, 2012 11:02 pm
- Forum: Number Theory
- Topic: An interesting LL problem of IMO 1971
- Replies: 4
- Views: 2837
Re: An interesting LL problem of IMO 1971
For some integers m and n, we have \[(m + 1)^{3} - m^{3}\ = 3m^{2}+3m+1=n^{^{2}}\] . So, \[12m^{2}+12m+4 = 4n^{_{2}}\], from which we can get \[3(2m+1)^{2}= (2n+1)(2n-1)\]. Now (2n+1) & (2n-1) are RELATIVELY PRIME. Since both are odd, their greatest common divisor must be 1. Then, we have two possib...
- Fri Feb 03, 2012 9:54 pm
- Forum: Secondary Level
- Topic: Solve this equation
- Replies: 2
- Views: 2353
Solve this equation
\[\frac{2}{3}[1+\frac{1}{1+x}+\frac{1}{(1+x)^{3}}+\frac{1}{(1+x)^{5}}+.........] = 1\]
- Mon Jan 02, 2012 12:24 am
- Forum: National Math Olympiad (BdMO)
- Topic: Number Set
- Replies: 2
- Views: 2446
Re: Number Set
81 solutions.