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i R e T R AT L e e e
LAt 3l e s T T I EI L PRERTETRE T I Te RS 3 d } ABHEHHNNNIG RN R I

96 THE FASCINATION OF NUMBERS

expressed as 076923, it will be seen to have properties similar
to those of 142857.

I X 076923 =076923

2 = 153846
3 =230769
4 =307692
5 = 384615
6 == 461538
7 o 538461
8 o 615384
9 =692307
10 =%769230
II = 846153
12 =923076

These results differ from those obtained in the multiplica-
tion of 142857 in that they give rise to numbers consisting
of two distinct sets of digits. Each set of digits, however, is
always repeated in the same cyclic order.

The numbers 142857 and 076923 have a common origin.
They each represent a cycle of recurring decimals which
result from the division of unity by a prime number (in these
cases, the primes are 7 and 13 respectively). Recurring deci-
mals are considered in more detail in the next chapter.