By H. F. Baker

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Are definite integers, does not affect + the sum, we clearly have, if m,, m^ be also integers, P , "'} p +m/ n = E (TO/) IE [v (k + p') + $T (k + /) +p (k + p')], = 2m/ and the second formula of 6 (v + / e m + rm t, (S) gives = e ~ 2 * im/ P> ; P'\ ; ] <" + *""'> + 2jri ^ ~ P> "' (v . ')]. = 2q n thus the function ; ; V = (2g-,, 1q, i (. ) j}/ In case the couplets we have e (,, ) + r* * = e- 2 " . , , ; (v [CHAP, and noting that the addition of integer. ,' an even integer ' 1 and in 1 is l shewn without when 2g and of even functions obtainable effectively the similarly the ; + x^x^ = odd difficulty that number which each of xlt thus easily found to be 10 found by solving x x^ is integer, 0ft;; ) and x^, number a;,', number is of solutions of zero or unity, of odd functions is #,' is effectively 6.

ART. 9] 21 integral functions. h as this is the . dam = dcrm'h = am adlnn dh, . same as = H= where Trira- ( and m + - dh --r r I } V this holds for arbitrary integer pairs h and m. */, h 2 choosing the integers m/, m/ suitably, with the condition (HI, Q^ft

Other and ar +ib r r The 1.

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