Find the remainder of the division 19122/17.
Explanation:
R[19122/17] = R[19/17]122 = R[2122/17]
Let us find the pattern that remainders follow when successive powers of 2 are divided by 17.
Remainder of 21/17 = 2. Remainder of 22/17 = 4. Remainder of 23/17 = 8. Remainder of 24/17 = 16 = -1.
∴ Remainder will repeat after every 8 terms.
or, R[24/17] = -1
⇒ R[2122/7] = R[24×30+2/7] = R[2120/7] × R[22/7] = R[24/7]30 × R[22/7] = (-1)30 × 4 = 4.
Hence, 4.
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