Let (a, b) denote the greatest common divisor (ged) of the numbers a and b. Let x ((61610+1,6171-...

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Let (a, b) denote the greatest common divisor (ged) of the numbers a and b. Let x ((61610+1,6171-1)61 +1, (61611,61671)610- 6

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Answer 1

Answer #1

Using property of exponential modular -

Property of Exponentiation in Modular Arithmetic Ifa b (mod N), then a* b (mod N) for any positive integer k.

Using this property, (61)⁶¹⁰ mod 10 = (61 mod 10)⁶¹⁰ = 1⁶¹⁰

X = ((1⁶¹⁰ + 1, 1⁶⁷¹ - 1)⁶⁷¹ + 1, (1⁶¹⁰ + 1, 1⁶⁷¹ - 1)⁶¹⁰ - 1 )

X = ( (2, 0)⁶⁷¹ + 1, (2, 0)⁶¹⁰ - 1 )

Since gcd of(a, 0) = 0

X = (0⁶⁷¹ + 1, 0⁶¹⁰ - 1)

X = (1, -1)

That is X = gcd of 1 and -1

X = 1

Hence X can be represented using only a single bit

I have tried to explain it in very simple language and I hope that i have answered your question satisfactorily.Leave doubts in comment section if any.

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Answer 2

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