- Hi

I think using the concepts of congruency and modulo will be much

helpful here. these, as you might be knowing, help you in calculating

these remainders in just 1 step, and there are also very powerful

short theorems in these topics.

in case you are not aware of these topics, you can get them in any

standard number theory textbook. you may also refer

http://mathworld.wolfram.com

bye.... all the best for CAT exams!

--

Siddharth Tallur

B.Tech Electrical Engineering

IIT Bombay

On 10/24/05, Mridul Sharma <it_edu2002@...> wrote:

>

> Hi Khushi,

>

> Answers to ur problems are as below,

>

> khushi shukla <ss11rd03@...> wrote:

>

>

>

> Remainder wen 6 to the power 45 + 6 to the power 3 is divided by 215

>

> a)0 b) 6 c)4 d)none of these

>

>

>

> (6^3)^15 + 6^3 can be written as (215+1)^ + (215+1) so when divided by 215

> will give remainder 1+1=2

>

>

>

> remainder wen 3 to the power 440 is divided by 15

>

> a)6 b) 4 c) 2 d)0

>

>

>

> 3^439/5 can be written as 3 .3^438/5 = 3.(3^2)^219=3.(10-1)^219 when divided

> by 5 gives remainder -3 that means +2 since we cancelled 3 thus remainder

> should be 6

>

> for any value of `P` prime number greatr tan 3 ,p to the power 2 +17

> divided by 24

>

> a)0 b) 1 c) 2 d)none of these

>

>

>

> This question requires clarity are u talking (p^2)+17 or p^2+17

>

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--

Siddharth Tallur

B.Tech Electrical Engineering

IIT Bombay - dear friends,i have a math question which is very interesting. i have been trying to get an answer but almost all efforts went in vain , so i seek your humble assitance to get the exact answer to this question which goes as follows:in a particular no system the product of 44 and 11 is 1034. what is the value of 3111 in decimal system?

Find out what India is talking about on - Yahoo! Answers India

Send FREE SMS to your friend's mobile from Yahoo! Messenger Version 8. Get it NOW - it will be for base system 5 , so value of 3111= 156

soln : (4n+4)*(n+1)=n^3+3*n+4On 9/26/06,**samir joshi**< sam_shill_143@...> wrote:dear friends,i have a math question which is very interesting. i have been trying to get an answer but almost all efforts went in vain , so i seek your humble assitance to get the exact answer to this question which goes as follows:in a particular no system the product of 44 and 11 is 1034. what is the value of 3111 in decimal system?

Find out what India is talking about on - Yahoo! Answers India

Send FREE SMS to your friend's mobile from Yahoo! Messenger Version 8. Get it NOW - Hi dear ,This can be the solution for ur problem:Lets say that number syatem is based on base n.Notationsnumber in base n= (no.)nnmber in base 10 = (no.)10(44)in base n = (4n+4) in base 10(11) in base n = (n+1) in base 10(1034) in base n = (1.n^3 + 3.n + 4 ) in base 10.(4n + 4) (n+1) = (n^3 + 3.n + 4)4n^2 + 8n + 4 = n^3 + 3n +4Solving this would given = 5,0,-1A base can't be -ve negative and 0So our numbers are in base 5.[3111] in base 10 = [44421] in base 5(n)Thanks and RegardsAnand

**From:**ascent4cat@yahoogroups.com [mailto:ascent4cat@yahoogroups.com]**On Behalf Of**samir joshi**Sent:**Tuesday, September 26, 2006 7:59 PM**To:**ascent4cat@yahoogroups.com**Subject:**[Ascent CAT] number systemdear friends,i have a math question which is very interesting. i have been trying to get an answer but almost all efforts went in vain , so i seek your humble assitance to get the exact answer to this question which goes as follows:in a particular no system the product of 44 and 11 is 1034. what is the value of 3111 in decimal system?

Find out what India is talking about on - Yahoo! Answers India

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- how many natural numbers less than 1700 can be expressed as the

difference of the two perfect squares in atleast one way.

a.)1174

b.)1274

c.)1374

d.)974