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Maybe some of the answers to this question about "eventual counterexamples" - ie, which could plausibly be true for all $n$ but which fail for some large number - are relevant?

Some highlights from that question:

• $gcd(n^5−5,(n+1)^5−5)=1$ is true for n=1,2,…,1435389 but not for n=1435390; and many similar
• factors of $x^n−1$ over the rationals have no coefficient exceeding 1 in absolute value - until $n=105$
• The Strong Law of Small Numbers, a fun paper by Guy

Maybe some of the answers to this question about "eventual counterexamples" - ie, which could plausibly be true for all $n$ but which fail for some large number - are relevant?

Some highlights from that question:

• $gcd(n^5−5,(n+1)^5−5)=1$ is true for n=1,2,…,1435389 but not for n=1435390; and many similar
• factors of $x^n−1$ over the rationals have no coefficient exceeding 1 in absolute value - until $n=105$
• The Strong Law of Small Numbers, a fun paper by Guy

Maybe some of the answers to this question about "eventual counterexamples" - ie, which could plausibly be true for all $n$ but which fail for some large number - are relevant?

Some highlights from that question:

• $gcd(n^5−5,(n+1)^5−5)=1$ is true for n=1,2,…,1435389 but not for n=1435390; and many similar
• factors of $x^n−1$ over the rationals have no coefficient exceeding 1 in absolute value - until $n=105$
• The Strong Law of Small Numbers, a fun paper by Guy

Maybe some of the answers to this question about "eventual counterexamples" - ie, which could plausibly be true for all $n$ but which fail for some large number - are relevant?

Some highlights from that question:

• $gcd(n^5−5,(n+1)^5−5)=1$ is true for n=1,2,…,1435389 but not for n=1435390; and many similar
• factors of $x^n−1$ over the rationals have no coefficient exceeding 1 in absolute value - until $n=105$
• The Strong Law of Small Numbers, a fun paper by Guy

Maybe some of the answers to this question about "eventual counterexamples" - ie, which could plausibly be true for all $n$ but which fail for some large number - are relevant?

Some highlights from that question:

• $gcd(n^5−5,(n+1)^5−5)=1$ is true for n=1,2,…,1435389 but not for n=1435390; and many similar
• factors of $x^n−1$ over the rationals have no coefficient exceeding 1 in absolute value - until $n=105$
• The Strong Law of Small Numbers, a fun paper by Guy

Maybe some of the answers to this question about "eventual counterexamples" - ie, which could plausibly be true for all $n$ but which fail for some large number - are relevant?

Some highlights from that question:

• $gcd(n^5−5,(n+1)^5−5)=1$ is true for n=1,2,…,1435389 but not for n=1435390; and many similar
• factors of $x^n−1$ over the rationals have no coefficient exceeding 1 in absolute value - until $n=105$
• The Strong Law of Small Numbers, a fun paper by Guy