Coloured numbers

Mussel wrote four different natural numbers with coloured markers: red, blue, green and yellow. When the red number divides by blue, it gets the green number as an incomplete proportion, and yellow represents the remainder after this division. When it divides the blue number by green, its division comes out without a remainder, and the share is the yellow number. Mussel revealed that two of her four numbers are 97 and 101. Identify the other Mussel numbers and assign colours to each number. Find all the options.

Correct result:

y =  97
g =  101
b =  9797
r =  989594
y1 =  101
g1 =  97
b1 =  9797
r1 =  950410

Solution:

97 ...  prime number 101 ...  prime number GCD(97,101)=1  d=GCD(97,101)=1 97 ...  prime number 101 ...  prime number LCM(97,101)=97101=9797  m=LCM(97,101)=9797  y=97
g=101
b=y g=97 101=9797
r=b g+y=9797 101+97=989594
y1=g=101
g1=y=97
b1=y1 g1=101 97=9797
r1=b1 g1+y1=9797 97+101=950410



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