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Omni-MATH / The Fibonacci sequence is defined as follows: F₀=0,F₁=1, and F_(n)=F_(n−1)+F_(n−2) for all integers n≥2. Find the smallest positive integer m such that F_{m} equiv 0(bmod 127) and …

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problem

The Fibonacci sequence is defined as follows: F0=0,F1=1F_{0}=0, F_{1}=1, and Fn=Fn−1+Fn−2F_{n}=F_{n-1}+F_{n-2} for all integers n≥2n \geq 2. Find the smallest positive integer mm such that $F_{m} \equiv 0(\bmod 127)$ and $F_{m+1} \equiv 1(\bmod 127)$.
Plain-text mathematical notation (without MathML)
The Fibonacci sequence is defined as follows: F₀=0,F₁=1, and F_(n)=F_(n−1)+F_(n−2) for all integers n≥2. Find the smallest positive integer m such that $F_{m} \equiv 0(\bmod 127)$ and $F_{m+1} \equiv 1(\bmod 127)$.
Original LaTeX notation
The Fibonacci sequence is defined as follows: $F_{0}=0, F_{1}=1$, and $F_{n}=F_{n-1}+F_{n-2}$ for all integers $n \geq 2$. Find the smallest positive integer $m$ such that $F_{m} \equiv 0(\bmod 127)$ and $F_{m+1} \equiv 1(\bmod 127)$.

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task_id
f8c4ff45-6426-549f-81b4-55ec7cf4cbed
task_key
test--f8c4ff45-6426-549f-81b4-55ec7cf4cbed
task_revision_id
1
config / split
/ test

Official source

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