Question:
The integer just greater than (3+√(5))²n is divisible by (n∈N)
The integer just greater than (3+√(5))²n is divisible by (n∈N)
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Expressions involving a+√(b) and a-√(b) often give integers when added.
Updated On: Mar 19, 2026
- 2ⁿ-1
- 2ⁿ+1
- 2ⁿ+2
- Not divisible by 2
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Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1:
(3+√(5))²n + (3-√(5))²n is an integer.
Step 2: Since 0<3-√(5)<1,
0<(3-√(5))²n<1
Step 3: Hence, the integer just greater than (3+√(5))²n is:
(3+√(5))²n+(3-√(5))²n
Step 4: This integer is divisible by 2ⁿ-1.
Therefore, option (A) is correct.
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