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# Magic Number

Posted on 2009-04-10
Medium Priority
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I have to write progarm for following problem -
File contain numbers. Numbers can be of 20 digits. I want to write program so that it can print number - with following property

75 * 75 * 75 = 421875 (last two digits are 75)
501 * 501 * 501 = 125751501 (again last 3 difits are same as 501)

Following numbers are also have same property
49999999999999999999
1787109375
12890625
4218751
2890624
3751

``````Please help me to solve this problem. I am sure strig need to use for it as there is no datatype that store number for 20 digits and its cube.
``````
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LVL 7

Accepted Solution

johnnash1180 earned 750 total points
ID: 24121276
Try out using the C++ big integer library available at http://mattmccutchen.net/bigint/

John Nash
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Expert Comment

ID: 24121282
You can get more details on large number arithmetic from the http://en.wikipedia.org/wiki/Arbitrary_precision_arithmetic URL.
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Assisted Solution

InteractiveMind earned 750 total points
ID: 24122079
The last three digits of n^3 only depend on the last three digits of n.

If n consists of a units, b tens, and c hundreds, then the last three digits of n^3 will be:

(a^3 + 3a^2*b*10 + 3a^2*c*100 + 2a*b^2*100) % 1000
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Expert Comment

ID: 24122124
(So, for example, read the number into a char[], cast the last three digits to integers, perform the above check. If it equals the last three digits then it's a 'magic number', so put the char[])
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