MathDB

Show that there exists a

10 \times 10

table of distinct natural numbers such that if

R_i

is equal to the multiplication of numbers of row

i

and

S_i

is equal to multiplication of numbers of column

i

, then numbers

R_1

R_2

, ... ,

R_{10}

make a nontrivial arithmetic sequence and numbers

S_1

S_2

, ... ,

S_{10}

also make a nontrivial arithmetic sequence. (A nontrivial arithmetic sequence is an arithmetic sequence with common difference between terms not equal to

0

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Problems(1)