Find the smallest positive integer whose fourth power ends in 01. - Sterling Industries
Find the smallest positive integer whose fourth power ends in 01
Find the smallest positive integer whose fourth power ends in 01
What number, when raised to the fourth power, leaves a trail ending in 01—like a quiet puzzle sparking quiet intrigue? That’s the mystery behind finding the smallest positive integer whose fourth power ends in 01. This question isn’t just academic—it’s gaining quiet traction among curious minds exploring number patterns, digital curiosity, and pattern recognition in math. As online search trends reflect growing interest in cryptography, number theory, and computational puzzles, this specific end trait has emerged as a subtle but compelling edge case.
Why this question is resonating in the US digital space
Across the United States, curiosity about logic, puzzles, and digital secrecy is at an all-time high—amplified by digital literacy growth and growing fascination with data patterns. While not mainstream, finding the smallest integer whose fourth power ends in 01 taps into a broader cultural pattern: people are drawn to unsolved or minimally solvable problems that offer quiet satisfaction through discovery. This query aligns with trends in logic-based learning, educational sharing, and even emerging niche communities centered on structured problem-solving. Though seemingly niche, its precise nature makes it both memorable and shareable in informed forums and mobile-first discovery feeds.
Understanding the Context
How to determine the correct integer—step by step
To find the smallest positive integer ( n ) such that ( n^4 \mod 100 = 01 ), we focus on the last two digits of fourth powers. This depends on the units digit and tens digit of ( n ). We test small integers systematically, analyzing ( n^4 ) modulo 100.
Testing values from 1 upward reveals:
- ( 1^4 = 1 \rightarrow 01 ) (ends in 01!)
But wait—though mathematically correct, ( 1^4 = 1 ), ending in 01 only via zero padding, suggesting the search aims for two-digit suffix, not just unity.
Continuing:
- ( 11^4 = 14641 \Rightarrow ) ends in 41
- ( 21^4 = 194481 \Rightarrow 81 )
- ( 31^4 = 923521 \Rightarrow 21 )
- ( 41^4 = 2825761 \Rightarrow 61 )
- ( 51^4 = 6765201 \Rightarrow 01 👀
Key Insights
At ( n = 51 ), ( 51^4 = 6765201 ), confirming the last two digits are 01
