Dear Corey, Thank you so much for your guidance.

Dear Carol, I have tried to upvoting your answer the first time I read it and also now, But I get this answer in both times I tried: " Votes cast by those with less than 15 reputation are recorded, but do not change the publicly displayed post score.|

Dear Corey, Thank you so much. Thank you.

Dear Stitch, Thank you so much for your kind help.

Dear Corey979, Thank you so much for your kind help, I just can understand the last step (checking). What does this command do? "f[pp[d], d] // FullSimplify[#, d ∈ Integers] &"

Dear Jim Baldwin, Thank you so much for your guidance.

Thank you so much for your kind help.

Thank you so much for your kind help.

Dear corey979, Thank you so much for your guidance.

Dear Manuel --Moe-- G , Thank you so much for your helpful guidance.