Project ForgeDiscrete Mathematics
Number Theory & Modular Arithmetic
GATE 2008
Medium
Let r denote number system radix. The only value(s) of r that satisfy the equation √(121ᵣ) = 11ᵣ is/are
- Adecimal 10
- Bdecimal 11
- Cdecimal 10 and 11
- any value > 2
Explanation
In base r, 121ᵣ = r²+2r+1 = (r+1)², so √(121ᵣ) = r+1, which is exactly 11ᵣ (=1·r+1) in base r. This identity holds for EVERY valid radix r (the digit '2' just requires r≥3, i.e. r>2), not only 10 or 11.
Source: GATE CS 2008 (2008)
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