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## Henry Bushby Transcription pages

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[pencil]M qua factor of y=^{y}/_{D} where

D is any divisor of y^{y}/_{MN} = ^{y}/_{yN}/_{D} = ^{D}/_{N} = x

∴ when x = ^{D}/_{N} then [?]

[?] D = Nx & N = ^{D}/_{x} but II_{5} ^{4b}/_{15c}

∴ where y is divisible by Nx it [should?] suffice

[Top half of page overwritten with pen]

XXM qua factor of y = ^{y}/_{D} where D is

any divisor of y

∴ ^{y}/_{MN} = ^{y}/_{yN}/_{D} = ^{D}/_{N} = x ([?]x hypoth)

∴ x = ^{D}/_{N} , N = ^{D}/_{x} , D = Nx.

∴ where y is divisible by Nx it shld suffice

But II_{5} ^{4b}/_{16c} is irreducible though Nx=8 & y=16

∴ it is not true that M may be any factor of y.

And II_{5} ^{4b}/_{16c} also has in for x ^{16}/_{2×2} where

2 is a factor of II. ∴ it is not true that it may be of N.

S

_{7}

^{1b}/

_{6c}

^{2b}/

_{12c}

^{3b}/

_{18c}

^{4b}/

_{24c}

^{5b}/

_{30c}

^{6b}/

_{36c}

^{7b}/

_{42c}

II

_{7}

^{3b}/

_{18c}= II

_{7}

^{18}/

_{3×2}b/

_{18c}

Here 3 is the multiple, a factor of y &

not of II

2=GCM of 3 & y. None

∴ z=1.

Required therefore II

_{7}

^{3b/18c }