- #1
Leo Liu
- 353
- 156
- Homework Statement
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- Relevant Equations
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https://www.physicsforums.com/attachments/292386
I need to use the congruence to solve this question. My strategy is to write the question as a congruence and then simplify the congruence so that I can apply Congruence to remainder to get the remainder. My work is as follows:
We know that
##453\equiv 53 (mod\, 100)##
Thus,
##453^{234}\equiv 53^{234} (mod\, 100)## by Congruence Power.
Also since
##53^2\equiv 9 (mod\, 100)##,
##53^234\equiv 9^{117} (mod\, 100)##.
So by the transitivity property, we have
##453^{234}\equiv 3^{234} (mod\, 100)##
But I am stuck here. Can someone help me out, please?
I need to use the congruence to solve this question. My strategy is to write the question as a congruence and then simplify the congruence so that I can apply Congruence to remainder to get the remainder. My work is as follows:
We know that
##453\equiv 53 (mod\, 100)##
Thus,
##453^{234}\equiv 53^{234} (mod\, 100)## by Congruence Power.
Also since
##53^2\equiv 9 (mod\, 100)##,
##53^234\equiv 9^{117} (mod\, 100)##.
So by the transitivity property, we have
##453^{234}\equiv 3^{234} (mod\, 100)##
But I am stuck here. Can someone help me out, please?
