The value of the expression 1399 mod17, in the range 0 to 16, is …
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GATE CSE 2016 Set 2 · Q29
Time
Your answerNumerical answer
Solution
Official answer: 4
Discrete MathematicsBy Fermat's Little Theorem, if is prime and , then:
Here, and (which is prime). Thus:
We can decompose the exponent as:
Therefore:
Since :
Now, reducing modulo :
Thus, the value of the expression in the range 0 to 16 is 4.
Try the question first, then check your work.
Examiner trap
Apply Fermat's Little Theorem with to reduce the exponent modulo 16.
This Discrete Mathematics previous year question is Q29 of the GATE CSE 2016 Set 2 paper. Find more GATE CSE PYQs on Discrete Mathematics in Engineering Mathematics, or browse all GATE CSE PYQs.
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Discrete Mathematics has 50 GATE CSE PYQs across 23 papers from 2011 to 2026. 6 of them are 2-mark NAT questions like this one, and GATE CSE 2016 Set 2 has 4.
How GATE tests Discrete MathematicsIndependent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.