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Ask iit jee aieee pet cbse icse state board experts Expert Question: what is the remaider of 23 raise to 23 divided by 53
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hermionesron (0)

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what is the remaider of 23 raise to 23 divided by 53
    
hsbhatt (4968)

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Hint: look at 232

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sboosy (3063)

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23^0 = 1 \div 53 , R = 1 \\ \\ 23^1 = 23 \div 53 , R = 23 \\ \\ 23^2 = 529 \div 53 , R = 52 \\ \\ 23^3 = 12167 \div 53 , R = 30 \\ \\ 23^4 = 279841 \div 53 , R= 1  \\ \\ \mbox{Thus it repeats} \\ \\ 23^{23} \ \mbox{will have same remainder as} \ 23^3 \\ \\ \mbox{Thus} \ R = 30
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the.sniper (642)

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2323=23(23)22 = 23(529)11 = - 23(1-530)11 = -23(1+m530) = -23 + 530k = -23 + 530k +53-53 = 53(10k-1) + 30

thus on dividing by 53 the remainder is 30

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