Unique Properties of the Fibonacci and Lucas Sequences, by Stephen A. Parry
Good job—much better flow and writing than earlier version. Fix the following minor
problems, and it will be ready to publish.
Page 1.
Intro. “to create a ring that includes” (not: which includes”
Also, “relations among” (not: between).
Background. Second sentence; omit the comma, and change ‘which’ to ‘that.’
Page 2.
From what I read, there is only one example in the whole paper, so write Example instead
of Example 1.
Page 3.
Second to last sentence: omit the comma after the matrix.
Page 4.
First line: omit the comma after ‘implies.’
Remark 2: replace the word ‘one’ with the numeral 1.
Second to last sentence: general solution is (not general solutions are).
Last sentence: insert a comma after the R [set of reals], and delete the word ‘then’ right
after that.
Page 5.
In the statement of Theorem 5, delete the period in line 2, and insert a comma and the
word ‘and.’
Two-thirds of the way down the page: the sentence that begins, “We will now solve…” is
missing a word someplace.
Page 6.
First line: I could find only one corollary, so delete the numeral 1, since it’s the only
corollary in the whole paper.
In the proof, you don’t need to write DE three times.
Theorem 6: Insert a period after the matrix. Capitalize: Then.
The word ‘let’ should be capitalized.
“they are each a sum of squares” (not: they are the sum of squares).
Replace the word ‘zero’ in both places by the numeral 0.
Under that paragraph, write: = 0 once (at the end), not three times.