Modular exponentiation: Difference between revisions
Content added Content deleted
m (Added comment) |
m (added whitespace.) |
||
Line 1: | Line 1: | ||
{{task}} |
{{task}} |
||
Find the last 40 decimal digits of <math>a^b</math>, where |
Find the last '''40''' decimal digits of <math>a^b</math>, where |
||
* <math>a = 2988348162058574136915891421498819466320163312926952423791023078876139</math> |
::* <math>a = 2988348162058574136915891421498819466320163312926952423791023078876139</math> |
||
* <math>b = 2351399303373464486466122544523690094744975233415544072992656881240319</math> |
::* <math>b = 2351399303373464486466122544523690094744975233415544072992656881240319</math> |
||
<br> |
|||
A computer is too slow to find the entire value of <math>a^b</math>. |
|||
A computer is too slow to find the entire value of <math>a^b</math>. |
|||
Instead, the program must use a fast algorithm for [[wp:Modular exponentiation|modular exponentiation]]: <math>a^b \mod m</math>. |
|||
The algorithm must work for any integers <math>a, b, m</math>, where <math>b \ge 0</math> and <math>m > 0</math>. |
|||
<br><br> |
<br><br> |
||