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 A228760 Least positive integer x such that x and n*x are both differences of fourth powers. 1
 1, 179727600, 80, 1040, 16, 2320, 4080, 236187120, 76960, 240, 17680, 76960, 80, 1040, 1, 1, 15, 65520, 4851120, 224991600, 100880, 1728480, 27120, 1389920, 19578624, 1048560, 240, 2986560, 80, 80, 2465, 11232975, 65, 16, 80, 2320, 12240, 707200, 16, 6560 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS It's not obvious that a(n) exists for all n. a(967) > 8*10^15 (if it exists). - Donovan Johnson, Sep 04 2013 REFERENCES A. Choudhry, Indian J. pure appl. Math. 26(11) (1995), 1057-1061 LINKS Robert Israel and Donovan Johnson, Table of n, a(n) for n = 1..966 (first 205 terms from Robert Israel) Tito Piezas II, Is the quartic diophantine equation a^4+n*b^4 = c^4+n*d^4 solvable for any integer n? EXAMPLE For n = 3, 80 = 3^4 - 1^4 and 3*80 = 4^4 - 2^4. MAPLE T:= 10^12; N:= 100; # to get solutions with n*a(n)<=T and n <= N cmax := floor(fsolve('c'^4 - ('c'-1)^4 = T)); S:= {seq(seq(c^4 - a^4, a = ceil((max(0, c^4 - T))^(1/4))..c-1), c=1..cmax)}: for n from 1 to N do B:= S intersect map(`*`, S, n); if B <> {} then A[n]:= min(B)/n; printf("a[%d] = %d\n", n, A[n]); end if end do: # Robert Israel, Sep 02 2013 CROSSREFS Cf. A152044. Sequence in context: A127955 A047738 A079323 * A204529 A211239 A180464 Adjacent sequences: A228757 A228758 A228759 * A228761 A228762 A228763 KEYWORD nonn AUTHOR Robert Israel, Sep 02 2013 STATUS approved

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Last modified September 25 05:35 EDT 2023. Contains 365582 sequences. (Running on oeis4.)