

A094907


Number of different nontrivial twodigit cancellations of the form (xy)/(zx) = y/z in base n.


2



0, 0, 1, 0, 2, 0, 2, 2, 4, 0, 4, 0, 2, 6, 7, 0, 4, 0, 4, 10, 6, 0, 6, 6, 4, 6, 10, 0, 6, 0, 4, 8, 6, 6, 21, 0, 2, 6, 18, 0, 6, 0, 4, 18, 10, 0, 8, 10, 10, 12, 12, 0, 6, 16, 22, 14, 6, 0, 10, 0, 2, 12, 21, 12, 20, 0, 4, 10, 22, 0, 10, 0, 2, 12, 20, 14, 24, 0, 8, 24, 8, 0, 10, 28, 6, 6, 18, 0, 10
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OFFSET

2,5


COMMENTS

Trivial cancellations are of the form xx/xx=x/x, e.g. 44/44 = 4/4.


REFERENCES

Boas, R. P. "Anomalous Cancellation," Ch. 6 in Mathematical Plums (Ed. R. Honsberger). Washington, DC: Math. Assoc. Amer., pp. 113129, 1979.


LINKS

R. P. Boas, Anomalous Cancellation, The Two Year College Mathematics Journal, Vol. 3, No. 2 (Autumn 1972), 2124.


FORMULA

a(n)=0 if and only if n is prime.
a(n) is odd if and only if n is an even square. (End)


EXAMPLE

a(10) = 4 because we have the four nontrivial base10 cancellations 64/16 = 4/1, 65/26 = 5/2, 95/19 = 5/1, 98/49 = 8/4.


MATHEMATICA

a[n_]:= Length[(DeleteCases[ #1, {u_, u_, u_}] & )[ Position[Table[(n*x + y)/(n*z + x) == y/z, {x, 1, n  1}, {y, 1, x  1}, {z, 1, y  1}], True]]]


CROSSREFS



KEYWORD

nonn,base


AUTHOR

Rick Mabry (rmabry(AT)pilot.lsus.edu), Jun 16 2004


STATUS

approved



