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The Wonders of Arithmetic from Pierre Simon de Fermat
Год написания книги
2021
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+(ad?bc)
=(ac?bd)
+(ad+bc)
. We take two numbers 4 + 9 = 13 and 1 + 16 = 17. Their product will be 13?17 = 221 = (4 + 9) ? (1+16) = (2?1 + 3?4)
+ (2?4 ? 3?1)
= (2?1 ? 3?4)
+ (2?4 + 3?1)
= 14
+ 5
= 10
+ 11
; Now if 221
= (221
)
= 10793861
; then the required result will be 221
= (14
+ 5
)?10793861
= (14?10793861)
+ (5?10793861)
= 151114054
+ 53969305
= (10
+ 11
)?10793861
=(10?10793861)
+ (11?10793861)
=107938610
+ 118732471
; But you can go also the other way if you submit the initial numbers for example, as follows: 221
= (14
+ 5
)?(10
+ 11
) = (14?10 + 5?11)
+ (14?11 ? 5?10)
= (14?10 ? 5?11)
+ (14?11+5?10)
= 195
+ 104
= 85
+ 204
; 221
= 221
?221 = (195
+ 104
)?(10
+ 11
) = (195?10 + 104?11)
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