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Find the last two digits of the number (17)^10.

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Find the last two digits of the number (17)10.

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1 Answer

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(17)10 = (289)5 

= (290 – 1)5 

= 5C0 (290)5 – 5C1 (290)4 + ........ + 5C4 (290)1 – 5C5 (290)0 

= 5C0 (290)5 – 5C1 . (290)4 + .........5C3 (290)2 + 5 × 290 – 1 

= A multiple of 1000 + 1449 

Hence, last two digits are 49.

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