*Written on 5 October, 2000*

1) For 47^{9} =
1,119,130,473,102,767

but if you use excel to calculate, the figure will be 1,119,130,473,102,770.

I have tried 47^{9}, 48^{9},
49^{9}, ..., 64^{9}, and got similar errors, except some of

the numbers ending with 0.

Most probably, error starts from n^{x},
where n > 46 and x > 8.

2) For 139^{7} =
1,002,544,368,429,379

but if you use excel to calculate, the figure will be 1,002,544,368,429,380.

I have tried 139^{7}, 140^{7},
141^{7}, ..., 35535^{7}, and got similar errors, except

some of the numbers ending with 0.

Most probably, error starts from N^{Y},
where N > 138 and Y > 6.

3) For 317^{6} = 1,014,741,853,230,169

but if you use excel to calculate, the figure will be 1,014,741,853,230,170.

I have tried 317^{6}, 318^{6},
319^{6}, ..., 1519^{6}, and got similar errors, except

some of the numbers ending with 0.

Most probably, error starts from m^{z},
where m > 316 and z > 5.

4) For 5624^{4} = 1,000,417,426,149,376

but if you use excel to calculate, the figure will be 1,000,417,426,149,380.

I have tried 5624^{4}, 5625^{4},
5626^{4}, ..., 65535^{4}, and got similar errors, except

some of the numbers ending with 0.

Most probably, error starts from C^{d},
where C > 5623 and d > 3.

5) For 31,622,777^{2} =
1,000,000,025,191,729

but if you use excel to calculate, the figure will be 1,000,000,025,191,730.

I have tried 31,622,777^{2},
31,622,778^{2}, 31,622,779^{2}, ..., 31,686,133^{2},
and

got similar errors, except some of the numbers ending with 0.

Most probably, error starts from M^{a},
where M > 31,622,776 and a > 1.

P.S. Similar errors were obtained in Lotus 1-2-3.

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