SOLUTION: Formulate a conjecture for which natural number n the formula (a+b)^(n) = a^n + b^n holds in clock n. I don't have to prove the conjecture, just state it and suffices to consider

Question 27147: Formulate a conjecture for which natural number n the formula
(a+b)^(n) = a^n + b^n holds in clock n. I don't have to prove the conjecture, just state it and suffices to consider clock n for n< and equal to 10
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
SEE THE FOLLOWING EXAMPLE
-----------------------------------------
(a+b)^7 = a^7 + b^7 in clock 7
IN CLOCK 7 THE NUMBERS REPEAT CHANGE DIGITS AFTER 7
THAT IS 12=5(MOD7)...NUMBER TWELVE WILL BE REPRESENTED BY 5 THE REMAINDER AFTER DIVIDING 12 BY 7.
LET A=X(MOD7)......................I
AND B=Y(MOD7).......................II.......WHERE X AND Y ARE LESS THAN 7.
A+B=(X+Y)(MOD7).............FROM I+II
(A+B)^7={(X+Y)+(X+Y)+....7 TIMES}(MOD7)=7(X+Y)(MOD7)=(X+Y)(MOD7)............III
A^7=(X+X+X...7 TIMES)(MOD7)=(7X)(MOD7)=X(MOD7)......FROMM I ................IV
SIMILARLY..B^7=Y(M0D7).............FROM II..................................V
ADDING IV AND V WE GET
A^Y+B^7=X(M0D7)+Y(MOD7)=(X+Y)(MOD7).................................VI
HENCE FROM III AND VI WE GET
(a+b)^7 = a^7 + b^7 in clock 7

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