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Find the last two digits of 3 |
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Answer» ong>Step-by-step explanation: This is same as asking what is REMAINDER when 3 1997 ÷100 3 4 ≡81mod100 3 8 ≡61mod100 3 12 ≡41mod100 3 ≡21mod100 3 20 ≡1mod100 Now, 3 40 ,3 60 ,3 ,3 100 ,....,3 1980 all are ≡1mod100 We know 3 16 ≡21mod100 3 ≡21×3mod100 3 17 ≡63mod100 ∴3 1997 ≡3 1980 ×3 17
since, 3 1980 ≡1mod100 and 3 17 ≡63mod100 ∴3 1997 ≡63mod100 ∴ Last two digit is 63 |
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