Question about Casio FX991MS Scientific Calculator

# How can I find :11^27mod 29 using my CASIO fx-99IES

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### John Watson

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11^27 = 13,109,994,191,499,930,367,061,460,371 which is 29 digits long.

You can get this result from the Windows calculator (scientific view) by entering 11 and then pressing x^y 27 = . Then use Mod 29 = to get the result, which is 8.

Unfortunately the Casio fx-991ms (as with most other calculators) doesn't have nearly enough digits to cope with this type of calculation. You therefore need to split the calculation down into more manageable chunks, as follows, which works on most calculators:

First calculate 11^3 = 1,331 and work out Mod 29, which is 1,331 - 45×29 = 26.
Then calculate 26^3 = 17,576 and work out Mod 29, which is 17,576 - 606×29 = 2.
Finally calculate 2^3 = 8. Since this is less than 29, it is also the final answer as confirmed above.

This method can be used with any power number that can be factorised into numbers that don't cause the available digits of the display to overflow. In this case 27 = 3×3×3 so each step involves cubing the previous answer.

Posted on Jul 05, 2011

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